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<jats:title>Abstract</jats:title> <jats:p>Fast sausage modes (FSMs) in flare loops have long been invoked to account for rapid quasi-periodic pulsations (QPPs) with periods of order seconds in flare lightcurves. However, most theories of FSMs in solar coronal cylinders assume a perfectly axisymmetric equilibrium, an idealized configuration apparently far from reality. In particular, it remains to be examined whether FSMs exist in coronal cylinders with fine structures. Working in the framework of ideal magnetohydrodynamics (MHD), we numerically follow the response to an axisymmetric perturbation of a coronal cylinder for which a considerable number of randomly distributed fine structures are superposed on an axisymmetric background. The parameters for the background component are largely motivated by the recent IRIS identification of a candidate FSM in Fe <jats:sc>xxi</jats:sc> 1354 Å observations. We find that the composite cylinder rapidly settles to an oscillatory behavior largely compatible with a canonical trapped FSM. This happens despite that kink-like motions develop in the fine structures. We further synthesize the Fe <jats:sc>xxi</jats:sc> 1354 Å emissions, finding that the transverse Alfvén time characterizes the periodicities in the intensity, Doppler shift, and Doppler width signals. Distinct from the case without fine structuring, a nonvanishing Doppler shift is seen even at the apex. We conclude that density-enhanced equilibria need not be strictly axisymmetric to host FSM-like motions in general, and FSMs remain a candidate interpretation for rapid QPPs in solar flares.</jats:p>