Sleep support ingredients are dietary supplement and functional-food ingredients studied for their effects on falling asleep faster, staying asleep, and sleep quality. They fall into four practical classes: the chronobiotic hormone melatonin, amino acids (L-theanine, glycine, and GABA), botanicals (valerian, ashwagandha, saffron, and chamomile), and the mineral magnesium. Human evidence is most consistent, though still modest, for melatonin on sleep onset latency, for saffron and ashwagandha on subjective sleep quality after several weeks, and for glycine and L-theanine on sleep quality via relaxation rather than sedation. Magnesium and GABA have weaker, more mixed data, and much of the botanical evidence rests on small or heterogeneous trials. The two decisions that separate a viable product from a liability are formulation (melatonin dose uniformity and stability, magnesium mass load, and valerian odor) and claims strategy, which diverges sharply between the structure/function regime in the United States, the closed health-claims list in the European Union, and the United Kingdom, where melatonin is a medicine rather than a supplement.
Table of Contents
- What Counts as a Sleep Support Ingredient
- The Main Classes at a Glance
- How Sleep Support Ingredients Work
- Clinical Evidence: What Holds Up and What Does Not
- Typical Use Levels
- Formulation and Stability Considerations
- Quality, Standardisation, and Adulteration
- Regulatory Status: United States, European Union, and United Kingdom
- Certifications and Supplier Landscape
- Related and Alternative Ingredients
- Frequently Asked Questions
- Key Takeaways
- Sources
What Counts as a Sleep Support Ingredient
A sleep support ingredient, in a dietary supplement context, is a compound or botanical extract marketed to support one or more of three outcomes: reducing the time taken to fall asleep, improving sleep continuity, and improving perceived sleep quality. The term is a marketing grouping, not a regulatory class. Most of these ingredients sit inside the ordinary supplement and functional-food frameworks, with two important exceptions covered below: melatonin, which several regulators treat as a medicine, and several sedative botanicals that fall under herbal-medicine regimes. For a B2B audience, the useful way to organise the category is by chemistry and evidence base, because that drives dose, format, stability, and the claims a brand can defend. The ingredients covered here range from a single well-characterised hormone to complex botanical extracts whose activity depends on standardisation, and their human evidence runs from multiple randomised controlled trials (RCTs) to small pilots and largely traditional use. Honest framing of that gap is both a regulatory necessity and a procurement filter.
The Main Classes at a Glance
The sleep-ingredient space organises into four classes that differ in evidence maturity, regulatory treatment, and formulation behaviour, summarised below for shortlisting.
Table 1. Major sleep support ingredient classes (B2B summary).
| Class | Representative ingredients | Typical studied dose | Strongest human signal | Formulation watch-out |
|---|---|---|---|---|
| Chronobiotic hormone | Melatonin (and tart cherry as a food-form source) | 0.5-5 mg | Reduced sleep onset latency, longer total sleep [1] | Low-dose content uniformity; light and heat sensitivity |
| Amino acids | L-theanine, glycine, GABA | 200 mg; 3 g; ~100 mg | Sleep quality via relaxation (L-theanine [6]); shorter latency (glycine [7]) | Hygroscopicity; glycine mass load |
| Botanicals | Valerian, ashwagandha, saffron, chamomile | 400-600 mg; 600 mg; 28 mg; 500-600 mg | Subjective sleep quality after weeks (ashwagandha [12], saffron [14]) | Odor, bitterness, standardisation, adulteration |
| Mineral | Magnesium (bisglycinate, citrate, oxide) | 250-500 mg elemental | Small, inconsistent benefit in poor sleepers [16,17] | High elemental mass per dose; taste |
How Sleep Support Ingredients Work
Sleep support ingredients act through several distinct, largely class-specific mechanisms, most better characterised in preclinical models than confirmed in humans. Melatonin is a chronobiotic hormone that signals darkness through MT1 and MT2 receptors, shifting the timing of the circadian clock as much as it promotes sleep directly. Several amino acids act on inhibitory or thermoregulatory pathways: glycine is associated with a fall in core body temperature through peripheral vasodilation, a physiological cue for sleep onset, while GABA is the primary inhibitory neurotransmitter in the central nervous system.
L-theanine is associated with increased alpha-wave activity and a relaxed, non-sedated state, and it may raise GABA, serotonin, and dopamine signaling. Among botanicals, valerian constituents are thought to act on GABAergic and adenosine pathways, apigenin from chamomile binds the central benzodiazepine site on the GABA-A receptor as a partial agonist, and the actives in ashwagandha and saffron are proposed to modulate the stress axis and cortisol. Magnesium contributes to normal nervous-system function and has been proposed to modulate NMDA and GABA-A activity. These are proposed pathways rather than established human pharmacology, and for oral GABA in particular the mechanism is genuinely unsettled, as discussed below.
See and download our infographic on sleep support ingredients:
Clinical Evidence: What Holds Up and What Does Not
Melatonin
Melatonin has the largest and most consistent dataset in the category. A meta-analysis of 19 randomised, placebo-controlled trials in 1,683 subjects found that melatonin decreased sleep onset latency, increased total sleep time, and improved overall sleep quality, with effects that were modest but did not appear to fade with continued use [1]. The same analysis reported larger effects at higher doses and longer durations, so the common assumption that sub-milligram doses are always sufficient is not well supported. The practical caveat for the category is less about efficacy than identity: independent testing has repeatedly found large gaps between labeled and actual melatonin content, discussed under quality below.
L-theanine and glycine
The two best-supported amino acids improve sleep quality without acting as sedatives. In a four-week crossover RCT in 30 adults, 200 mg/day of L-theanine improved Pittsburgh Sleep Quality Index scores, including the sleep-latency and sleep-disturbance subscales, an effect attributed to reduced anxiety rather than sedation [6]. Glycine has a smaller but mechanistically interesting evidence base: bolus doses of 3 g before bed in poor sleepers improved subjective sleep quality, shortened polysomnographic latency to both sleep onset and slow-wave sleep, and reduced next-day sleepiness in small crossover studies [7]. Both are best positioned as gentle, relaxation-oriented actives rather than strong hypnotics, and evidence that L-theanine supports relaxation continues to accumulate alongside its cognitive data.
GABA
Oral GABA is widely used but weakly supported, and its central mechanism is contested. A systematic review concluded that human evidence for a sleep benefit is very limited, with some support for reduced sleep latency after one to four weeks of use and no clear benefit for sleep maintenance, drawn from small, short, and often industry-linked trials [8]. A deeper problem sits underneath the outcome data: whether ingested GABA crosses the blood-brain barrier in humans is unresolved, and any behavioral effect may act indirectly through the gut-brain (enteric and vagal) axis rather than by raising brain GABA directly [9]. The defensible position is that GABA may support relaxation in some users, with a mechanism that is not established.
Valerian
Valerian shows modest and inconsistent effects. A meta-analysis of 16 RCTs in 1,093 patients concluded that valerian might improve subjective sleep quality, but cautioned that the studies were small, heterogeneous, and often of poor quality, with roughly half reporting no benefit [10]. Preparation and dose varied widely across trials, which limits read-across between products. Valerian is also frequently combined with hops or lemon balm, and its regulatory treatment in Europe differs from that of a typical food-supplement ingredient, as noted below.
Ashwagandha and saffron
The two botanicals with the cleaner recent RCT signal are ashwagandha and saffron. A meta-analysis of five RCTs in 400 participants found a small-to-moderate, statistically significant improvement in sleep with standardised ashwagandha extract (standardised mean difference around −0.59), with effects more prominent at doses of at least 600 mg/day, durations of at least eight weeks, and in adults diagnosed with insomnia [12]. Saffron has a supportive multi-week RCT: 28 mg/day of a standardised extract over 28 days improved Insomnia Severity Index and restorative-sleep scores versus placebo in adults with self-reported poor sleep [14]. Both effects are modest, both depend heavily on the specific standardised grade used, and ashwagandha carries regulatory constraints in several European markets that can override its evidence, covered below.
Read our article on the latest findings about saffron:
Saffron Extract Supports Mood and Self-Esteem in Menopausal Women
Chamomile and magnesium
Chamomile and magnesium round out the category with thinner or more mixed evidence. A pilot RCT of 270 mg of standardised chamomile twice daily for 28 days in chronic insomnia produced only modest, largely non-significant sleep-diary improvements, so its use rests as much on the apigenin-GABA-A mechanism and tradition as on trial data [15]. Magnesium evidence is genuinely mixed: an older 500 mg/day RCT in 46 elderly adults with insomnia reported improvements across subjective and some objective measures but was methodologically weak [16], and a more recent trial of magnesium bisglycinate at 250 mg elemental in 155 poor sleepers found a statistically significant but small reduction in insomnia severity, with the largest benefit in those with low dietary magnesium intake [17]. Magnesium is therefore best positioned for defined-deficiency or low-intake subgroups rather than broad sleep enhancement.
Typical Use Levels
Effective doses in trials often differ from typical commercial amounts, and for standardised botanicals the marker content matters more than the extract weight.
Table 2. Studied versus typical commercial dose ranges for selected sleep ingredients.
| Ingredient | Trial-supported dose | Typical commercial dose | Note |
|---|---|---|---|
| Melatonin | 0.5-5 mg | 1-10 mg | EU claim conditioned on 1 mg (fall asleep) or 0.5 mg (jet lag) [3] |
| L-theanine | 200 mg | 100-200 mg | Non-sedating; relaxation-oriented [6] |
| Glycine | 3 g | 3 g | Large mass; sweet taste aids formats [7] |
| GABA | ~100 mg | 100-200 mg | Weak, unsettled evidence [8] |
| Ashwagandha | 300-600 mg standardised | 300-600 mg | Match to withanolide content; restricted in some EU states [12,13] |
| Saffron | 28 mg standardised | 28 mg | Match to crocin/safranal markers [14] |
| Magnesium | 250-500 mg elemental | 100-350 mg elemental | EU supplemental UL 250 mg for dissociable salts [18] |
Formulation and Stability Considerations
Formulation is where sleep products most often fail in practice, because the category has drifted heavily toward gummies, which are one of the least forgiving formats for these actives. Melatonin is the clearest example. It is dosed at the milligram level, which makes content uniformity difficult, and it is sensitive to light and heat, so high-temperature gummy cooks and clear packaging both risk loss of active. The documented pattern of melatonin products measuring well above or below label (see quality, below) is in large part a manufacturing and stability problem, and it is most acute in melatonin and multi-ingredient sleep gummies, where overages are often added to compensate for degradation.
Magnesium presents the opposite problem: mass. A meaningful elemental dose is hundreds of milligrams, which is hard to fit into a single gummy or small capsule, and magnesium salts carry a bitter, metallic, or salty taste. Form selection is a bioavailability and tolerability decision as much as a cost one, which is why chelated forms such as magnesium bisglycinate and delivery approaches such as microencapsulated magnesium have gained ground over magnesium oxide for sleep and relaxation products.
Botanicals add sensory and stability constraints. Valerian has a strong isovaleric-acid odor that requires masking or encapsulation, and its combination with hops and lemon balm compounds the sensory challenge. Saffron and standardised extracts must be protected against marker degradation, and poorly water-soluble actives such as the chamomile flavonoid apigenin often need enabling delivery systems: work on apigenin solubility has raised its aqueous solubility by several orders of magnitude. Glycine is comparatively easy, with a sweet taste that suits powders and stick-packs, but its 3 g dose again runs into format mass limits. Across the category, capsules, tablets, powders, stick-packs, and nighttime functional beverages generally protect labile actives better than gummies, and format choice should follow the active, not the marketing trend.
Quality, Standardisation, and Adulteration
Quality control for sleep ingredients turns on identity, assay, and, for botanicals, standardisation markers, and several carry well-documented risks a certificate of analysis must address. Melatonin is the headline case: an analysis of 25 US melatonin gummy products found 22 (88%) inaccurately labeled, with measured melatonin ranging from 74% to 347% of the declared amount and one product containing no detectable melatonin at all [2]. For a category sold on a precise milligram dose, that is a specification and stability failure, not a minor labeling issue, and it argues for validated assay on finished product rather than reliance on raw-material certificates.
Botanicals carry their own risks:
- Saffron: one of the most adulterated commodities in the trade, commonly bulked with other plant material or dyes, so species and marker identity (crocins, safranal) must be confirmed, not assumed.
- Ashwagandha: demands a named withanolide standardisation with a specified method, because reliable adaptogen standardisation determines both the delivered dose and whether the clinical read-across to a studied grade holds.
- Valerian: activity is not fully explained by any single marker, so valerenic-acid content is a consistency check rather than a guarantee of effect, and preparation method must be specified.
- Across botanicals: require species-level identity by DNA barcoding or high-performance thin-layer chromatography (HPTLC) alongside marker HPLC, since title and appearance are not sufficient proof.
Compendial references support these checks: USP, the USP Food Chemicals Codex, and the European Pharmacopoeia carry relevant monographs and contaminant chapters covering heavy metals, microbial limits, pesticides, and residual solvents.
Regulatory Status: United States, European Union, and United Kingdom
Regulatory status, not science, is usually the deciding factor in what a brand can say and where an ingredient can be sold, and the three major English-language markets diverge sharply. In the United States, the Dietary Supplement Health and Education Act (DSHEA) treats supplements as a category of food with no premarket approval. Brands may make structure/function claims such as “supports restful sleep” or “helps you relax before bedtime” provided they hold substantiation, notify the Food and Drug Administration (FDA) within 30 days of marketing, and carry the mandatory disclaimer that the statement is not evaluated by the FDA [19]. The hard line is disease: because insomnia is a diagnosable disease, a claim to “treat insomnia” converts a supplement into an unapproved drug, whereas a sleep-quality or relaxation claim does not. Advertising is policed separately by the Federal Trade Commission (FTC) under its “competent and reliable scientific evidence” standard, which generally expects randomised, controlled human trials for effect claims [20].
The European Union runs a closed system under Regulation (EC) 1924/2006, where only claims on the EU Register may be used. Melatonin is the rare winner here, carrying two authorised claims: “reduction of time taken to fall asleep” conditioned on 1 mg per portion, and “alleviation of subjective feelings of jet lag” conditioned on 0.5 mg [3]. Magnesium carries authorised claims for normal nervous-system and psychological function and for reduction of tiredness and fatigue, but no direct sleep claim [3]. Most botanical sleep claims sit unresolved in the large “on hold” pool and cannot be used, and several sedative botanicals are handled as traditional herbal medicines instead of food supplements: valerian, for example, has a European Medicines Agency herbal monograph for mild nervous tension and to aid sleep, which is a medicinal pathway, not a supplement claim [11].
Two further constraints can block an ingredient before claims arise. In the United Kingdom, melatonin is a prescription-only medicine and is not permitted in food supplements at all, so a product lawful in the United States cannot cross to the UK shelf unchanged [4]. And ashwagandha now faces active safety scrutiny in the EU: Denmark has banned it in food supplements after a risk assessment could not establish a safe intake, France’s ANSES has warned vulnerable groups against use, the Netherlands has published a risk assessment, and EU food-safety agencies have prioritised it for review over liver, thyroid, and reproductive concerns [13]. Ashwagandha should therefore be treated as a sensitive ingredient, with country-by-country status confirmed before launch.
Certifications and Supplier Landscape
Procurement decisions for sleep ingredients increasingly hinge on certifications and grade provenance rather than price alone. Buyers commonly request USDA or EU organic, Non-GMO Project verification, kosher, halal, vegan, and allergen declarations, and, for wild-collected or heavily traded botanicals such as saffron and valerian, documented identity and origin. Whole-formulation certifications such as vegan and kosher can fail on a capsule shell or excipient even when the active complies, so they must be assessed at the finished-product level.
On the supply side, branded, clinically studied grades carry a specific advantage in this category, because much of the human evidence was generated on particular standardised extracts rather than on generic material. A label leaning on ashwagandha’s or saffron’s trial data is on firmer ground when the studied grade is the one in the bottle, and for melatonin the priority is a supplier and finished-product testing regime that can hold the labeled dose within specification. Extraction method and marker standardisation should appear on the specification alongside contaminant results, and for magnesium the specification should state both the salt and the elemental content, since these drive dose, tolerability, and mass.
Related and Alternative Ingredients
Brands building sleep formulations frequently pair or substitute the core actives above with adjacent ingredients. Tart cherry is a food-form source of melatonin and tryptophan, with an RCT reporting higher urinary melatonin and longer sleep after supplementation [5]. Other botanicals used mainly on traditional-use grounds or in combination include lemon balm (Melissa officinalis), passionflower (Passiflora incarnata), hops (Humulus lupulus), and magnolia bark. The serotonin and melatonin precursors L-tryptophan and 5-hydroxytryptophan (5-HTP, from Griffonia simplicifolia) appear in some formulations, and combination products such as ashwagandha and valerian sleep gummies are common, though stacking actives multiplies both the sensory challenges and the claims-substantiation burden.
Frequently Asked Questions
Which sleep ingredient has the strongest human evidence? Melatonin has the largest randomised-trial base for reducing the time taken to fall asleep and increasing total sleep time, though the effects are modest [1]. Saffron and ashwagandha have supportive multi-week RCTs for subjective sleep quality [12,14], and L-theanine and glycine improve sleep quality mainly through relaxation [6,7]. Evidence strength should be matched to the specific claim and market rather than generalised across the category.
Can a brand claim a supplement helps you sleep? In the United States, a structure/function claim such as “supports restful sleep” is permitted with substantiation, FDA notification, and the mandatory disclaimer, but a claim to treat insomnia is a prohibited disease claim [19,20]. In the European Union, only claims on the EU Register are allowed: melatonin has two authorised sleep and jet-lag claims, while most botanicals do not [3]. The permitted wording depends entirely on the market.
Why is melatonin treated differently in the UK and EU? In the United Kingdom, melatonin is a prescription-only medicine and cannot be sold as a food supplement [4]. In the European Union, it is permitted in supplements and even carries authorised claims at defined doses [3]. In the United States, it is a freely sold dietary supplement, which is why a single melatonin product cannot use one label across all three markets.
What is the main quality risk with melatonin gummies? Label accuracy. Independent testing found the large majority of melatonin gummy products contained substantially more or less melatonin than declared, with some far above label [2]. The dominant causes are milligram-level dose uniformity and degradation of a light- and heat-sensitive active during gummy manufacture, so validated finished-product assay is essential.
Is ashwagandha safe to use in any market? Not without checking. Ashwagandha has an encouraging sleep evidence base [12], but it is under active regulatory scrutiny in Europe: it is banned in food supplements in Denmark, carries an ANSES warning in France for vulnerable groups, and has been prioritised for EU safety review [13]. It should be treated as a sensitive ingredient with country-by-country status confirmed before launch.
Key Takeaways
Sleep ingredients group into the chronobiotic hormone melatonin, amino acids (L-theanine, glycine, GABA), botanicals (valerian, ashwagandha, saffron, chamomile), and the mineral magnesium, each with a different evidence and regulatory profile.
Human evidence is most consistent, though modest, for melatonin on sleep latency, and for saffron and ashwagandha on subjective sleep quality after several weeks; magnesium and GABA are weaker and more mixed.
Formulation success depends on managing melatonin dose uniformity and stability, magnesium mass load, and valerian odor, and gummies are among the least forgiving formats for these actives.
Melatonin label accuracy is a documented, category-wide quality risk that argues for validated finished-product assay.
Claims and market access diverge sharply: US structure/function versus the EU closed list, with melatonin a UK medicine and ashwagandha restricted in several EU states.
Sources
- Ferracioli-Oda E, Qawasmi A, Bloch MH. Meta-analysis: melatonin for the treatment of primary sleep disorders. PLoS One, 2013.
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0063773(accessed 2026-07-06). - Cohen PA, et al. Quantity of melatonin and CBD in melatonin gummies sold in the US. JAMA, 2023.
https://jamanetwork.com/journals/jama/fullarticle/2804077(accessed 2026-07-06). - European Commission. EU Register of nutrition and health claims (Regulation (EC) 1924/2006; Regulation (EU) 432/2012).
https://ec.europa.eu/food/food-feed-portal/screen/health-claims/eu-register(accessed 2026-07-06). - UK Medicines and Healthcare products Regulatory Agency (MHRA) / GOV.UK. Melatonin is a prescription-only medicine in the UK.
https://www.gov.uk/government/news/parents-and-caregivers-advised-to-stop-all-use-of-specific-brand-of-kids-magnesium-gummies-due-to-the-presence-of-an-undeclared-prescription-only-med(accessed 2026-07-06). - Howatson G, et al. Effect of tart cherry juice (Prunus cerasus) on melatonin levels and enhanced sleep quality. European Journal of Nutrition, 2012.
https://link.springer.com/article/10.1007/s00394-011-0263-7(accessed 2026-07-06). - Hidese S, et al. Effects of L-theanine administration on stress-related symptoms and cognitive functions in healthy adults: a randomized controlled trial. Nutrients, 2019.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6836118/(accessed 2026-07-06). - Yamadera W, et al. Glycine ingestion improves subjective sleep quality in human volunteers, correlating with polysomnographic changes. Sleep and Biological Rhythms, 2007.
https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1479-8425.2007.00262.x(accessed 2026-07-06). - Hepsomali P, et al. Effects of oral gamma-aminobutyric acid (GABA) administration on stress and sleep in humans: a systematic review. Frontiers in Neuroscience, 2020.
https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2020.00923/full(accessed 2026-07-06). - Boonstra E, et al. Neurotransmitters as food supplements: the effects of GABA on brain and behavior. Frontiers in Psychology, 2015.
https://pmc.ncbi.nlm.nih.gov/articles/PMC4594160/(accessed 2026-07-06). - Bent S, et al. Valerian for sleep: a systematic review and meta-analysis. American Journal of Medicine, 2006.
https://pmc.ncbi.nlm.nih.gov/articles/PMC4394901/(accessed 2026-07-06). - European Medicines Agency, Committee on Herbal Medicinal Products. Valerianae radix (Valeriana officinalis L., radix) herbal monograph.
https://www.ema.europa.eu/en/medicines/herbal/valerianae-radix(accessed 2026-07-06). - Cheah KL, et al. Effect of Ashwagandha (Withania somnifera) extract on sleep: a systematic review and meta-analysis. PLoS One, 2021.
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0257843(accessed 2026-07-06). - Phytotherapy Research. Ashwagandha (Withania somnifera): is it safe? A regulatory review documenting EU actions (Denmark ban, France ANSES warning, Netherlands assessment). 2025.
https://onlinelibrary.wiley.com/doi/10.1002/ptr.70151(accessed 2026-07-06). - Lopresti AL, et al. Effects of saffron on sleep quality in healthy adults with self-reported poor sleep: a randomized, double-blind, placebo-controlled trial. Journal of Clinical Sleep Medicine, 2020.
https://pmc.ncbi.nlm.nih.gov/articles/PMC7849671/(accessed 2026-07-06). - Zick SM, et al. Preliminary examination of the efficacy and safety of a standardized chamomile extract for chronic primary insomnia: a randomized placebo-controlled pilot study. BMC Complementary and Alternative Medicine, 2011.
https://pmc.ncbi.nlm.nih.gov/articles/PMC3198755/(accessed 2026-07-06). - Abbasi B, et al. The effect of magnesium supplementation on primary insomnia in elderly: a double-blind placebo-controlled clinical trial. Journal of Research in Medical Sciences, 2012.
https://pubmed.ncbi.nlm.nih.gov/23853635/(accessed 2026-07-06). - Schuster J, et al. Magnesium bisglycinate supplementation in healthy adults reporting poor sleep: a randomized, placebo-controlled trial. Nature and Science of Sleep, 2025.
https://www.tandfonline.com/doi/full/10.2147/NSS.S524348(accessed 2026-07-06). - European Food Safety Authority. Overview on tolerable upper intake levels: magnesium (supplemental UL 250 mg/day for readily dissociable salts).
https://www.efsa.europa.eu/sites/default/files/2024-05/ul-summary-report.pdf(accessed 2026-07-06). - US Food and Drug Administration. Structure/Function Claims (21 CFR 101.93).
https://www.fda.gov/food/nutrition-food-labeling-and-critical-foods/structurefunction-claims(accessed 2026-07-06). - US Federal Trade Commission. Health Products Compliance Guidance, 2022.
https://www.ftc.gov/business-guidance/resources/health-products-compliance-guidance(accessed 2026-07-06).
These statements have not been evaluated by the Food and Drug Administration. This information is provided for dietary supplement industry professionals and is not intended to diagnose, treat, cure, or prevent any disease.
Read more here:
Ingredients for fat burning, GLP-1 release, calorie, sugar & fat reduction
