Summary: In models of production theory and efficiency analysis, the inputs and outputs are assumed to satisfy some form of disposability. In this paper, we consider the assumption of weak input disposability. It states that any activity remains feasible if its inputs are simultaneously scaled up in the same proportion. As suggested in the literature, the Shephard technology incorporating weak input disposability could be used to evaluate the effect of input congestion. We show that the Shephard technology is not convex and therefore introduces bias in evaluation of congestion. To address this, we develop an alternative convex technology whose use in the evaluation of congestion removes the noted bias. We undertake a further axiomatic investigation and obtain a range of production technologies, all of which exhibit weak input disposability but are based on different, progressively relaxed, convexity assumptions. Apart from the evaluation of input congestion, such technologies should also be useful in applications in which some inputs are closely related or are overlapping, and therefore satisfy only the weak input disposability assumption incorporated in the new models.