The first three species in the key, with 2-cleft styles and lenticular or biconvex achenes, are frequently separated into the genus Pycreus.
1. Styles 2-cleft; achenes lenticular or biconvex; anthers 0.3–0.5 (–0.6) mm long.
2. Fully mature achene black with whitish incrustation in transverse lines, the surface cells (under high magnification) several times as long as wide; scales not over 2 (–2.2) mm long, yellow.
2. Fully mature achenes drab or brown, the whitish incrustation, if present, more delicate and often ± evenly reticulate, the surface cells not conspicuously elongate (not more than twice as long as wide); scales mostly 2–2.5 (–3) mm long, prominently marked with reddish (occasionally some entirely pale greenish white).
3. Reddish color of scales concentrated near the apex, usually prolonged toward base of scale in narrow bands bordering edge and midrib; style ± persistent, conspicuous at maturity of spikelet.
3. Reddish color of scales concentrated near the base and toward the edge, sometimes extending to apex and throughout the sides; style deciduous, often not conspicuous at maturity of spikelet.
1. Styles 3-cleft; achenes 3-sided; anthers various.
4. Tips of scales definitely spreading outward; stamen 1.
5. Scales merely acute and spreading at the tip; anthers ca. 0.5–0.7 mm long; sides of scales distinctly cellular, at most with one obscure nerve.
5. Scales with a narrowly acuminate or awn-like spreading-recurving tip ca. 0.5 mm long; anthers ca. 0.2–0.3 mm long; sides of scales distinctly ribbed or nerved.
4. Tips of scales not spreading, the backs of the scales ± straight (or slightly incurved) from base to apex; stamens 2–3.
6. Inflorescence (or inflorescence branches) with spikelets at maturity spreading-ascending in a cluster or forming a spherical head with a short central axis less than 1 (–1.5) cm long, rachilla wingless or at most with a very narrow wing; anthers 0.5–1.1 mm long (ca. 0.2 in the diminutive wetland alien C. fuscus).
7. Spikelets at maturity 1.1–1.5 (–1.7) mm wide, scales reddish purple; anthers ca. 0.2 mm long; fibrous-rooted annual of moist ground.
7. Spikelets at maturity mostly 1.5–5 mm wide, scales green to brown; anthers 0.3–1.1 mm long; perennials from a hard knotty rhizome, of dry usually sandy habitats (except C. iria).
8. Scales 1.2–1.8 mm long; achenes ca. 1.2–1.4 mm long; alien of wet to mesic disturbed habitats.
8. Scales ca. 2–4 mm long; achenes ca. 1.6-2.5 mm long; native plants of dry usually sandy habitats.
9. Culms 1–2.5 mm thick below the inflorescence, ± antrorsely scabrous on the sides and sharp angles; margins of involucral and cauline leaves scabrous; blades of broadest cauline leaves 3–5 mm wide; achenes (2–) 2.2–2.5 mm long; larger scales 3–4 mm long, including (at least on upper scales) an awn-like tip ca. 0.5–1 mm long.
9. Culms 0.4–1 (–1.2) mm thick below the inflorescence, smooth, rather obtusely angled; margins of leaves various; broadest cauline blades 1–3 mm wide (or rarely to 5 mm in C. houghtonii); achenes 1.6–2 mm long (not including tiny style base); scales 2–3 mm long, including a tiny tip less than 0.5 mm long (or this absent).
10. Involucral leaves strongly ascending, slightly scabrous or smoothish toward base; cauline leaves smooth or nearly so; inflorescence hemispherical or (usually) narrower, with loosely ascending spikelets (often 1–7 similar inflorescences on separate rays).
10. Involucral leaves mostly widely spreading or recurved at maturity, the margins of these and of the cauline leaves scabrous; inflorescence a dense hemispherical head (occasionally 1 or 2 similar inflorescences on separate rays).
6. Inflorescence (or inflorescence branches) with spikelets at maturity pinnately arranged ± at right angles to a distinct central axis often over 1 cm long, rachilla rather distinctly winged; anthers 0.2–0.6 mm (except 0.6–1.7 mm in C. esculentus with numerous slender scaly rhizomes).
11. Scales not overlapping on the same side of spikelet (the tip of one scale not quite reaching the base of the next above it).
11. Scales overlapping (the tip of each overlapping the base of the next one above it on the same side of spikelet).
12. Scales (3–) 3.5–4.5 (–5) mm long, with yellowish golden sides and greenish midrib; plants usually with hard knotty corm-like rhizomes.
12. Scales 1.1–2.7 mm long, often marked with reddish or dark brown; plants fibrous-rooted (but often large) annuals or (C. esculentus) perennials with numerous slender scaly rhizomes.
13. Wings of rachilla chaff-like, readily deciduous at maturity; achenes ca. 0.7–0.8 mm long; scales 1.1–1.5 (–1.6) mm long.
13. Wings of rachilla not separating; achenes ca. 1.1–1.4 mm long; scales (1.5–) 1.7–2.7 mm long.
14. Anthers (0.6–) 0.8–1.5 (–1.7) mm long at maturity; plants with numerous slender scaly rhizomes (these ultimately producing tubers); achenes (often poorly developed) only slightly covered by the wings of the rachilla; rachilla not disarticulating into segments.
14. Anthers 0.2–0.6 mm long; plants fibrous-rooted, without scaly rhizomes; rachilla wings embracing much of the basal half of the achenes; rachilla disarticulating between the achenes.