Encouraged by recent advances in radially-polarized laser technology, simulations have been performed of electron acceleration by a tightly-focused, ultra-short pulse in a parabolic plasma micro-channel. Milli-joule laser pulses, generated at kHz repetition rates, are shown to produce electron bunches of MeV energy, pC charge, low emittance and low divergence. The pivotal role played by the channel length in controlling the process is demonstrated, and the roles of direct and wakefield acceleration are distinguished.