This paper considers linear, binary codes having locality parameter r, that are capable of recovering from t ≥ 2 erasures and which additionally, possess short block length. Both parallel (through orthogonal parity checks) and sequential recovery are considered here. In the case of parallel repair, minimum-block-length constructions are characterized whenever t|(r 2 + r) and examples examined. In the case of sequential repair, the results include (a) extending and characterizing minimum-block-length constructions for t = 2, (b) providing improved bounds on block length for t = 3 as well as a general construction for t = 3 having short block length, (c) providing high-rate constructions for (r = 2, t ∈ {4, 5, 6, 7}) and (d) providing short-block-length constructions for general (r, t). Most of the codes constructed here are binary codes.