Abstract An experimental investigation and a theoretical appraisal are presented which enlarge upon previous observations of multiple steady flows in a Taylor apparatus where the fluid-filled annulus is comparatively short. The aim of the experiments was a systematic exploration of all anomalous modes in this apparatus, namely those stable flows that exist only at sufficiently high Reynolds number R and are always distinct from the primary flow developed by gradually increasing R from small values. Having been established at high R, an anomalous mode will always collapse eventually if R is then gradually reduced. The theoretical material bearing on the interpretation of the experi­ments is reviewed in §2, where mathematical details are largely deferred but several new conclusions are demonstrated. In particular, some curious facts are revealed about the limits of stability for anomalous modes comprising even numbers of Taylor cells, and about the properties of flows comprising a single cell only. Following a description of the apparatus in § 3, which includes an account of several improvements that have been introduced since the earlier experiments, the new experimental results are reported in § 4. They include stability curves (critical R against aspect ratio of annulus) for anomalous modes consisting of from two to seven Taylor cells (§ 4.1), observations on collapse routes for all these modes (§ 4.3), and measurements of various phenomena exhibited by the single-cell mode (§ 4.5). These and other phenomena recorded here for the first time are seen to accord with the theoretical prospectus.