A flexible, non-linear, unit-level sortation system for sorting mixed collections of items into orders. Collections of unsorted items for fulfilling requests are delivered to one or more singulation stations. At a singulation station, individual units of items are selected from a collection, associated with particular conveyance receptacles, and placed into the receptacles, with one and only one unit per receptacle. The receptacles may be inducted into a conveyance mechanism under the direction of a control system. The receptacles are not fixed to the conveyance mechanism. The control system may direct the conveyance mechanism to route the receptacles to a particular one of one or more sorting stations. At a sorting station, the units may retrieved from receptacles and placed into locations corresponding to particular orders under control or direction of the control system. The conveyance mechanism may, but does not necessarily, return empty conveyance receptacle to a singulation station.