This paper solves the problem of determining fixed but allocatable input allocations by dual methods. A flexible, profit function approach for estimating input‐nonjoint technologies with allocatable fixed factors is developed. Variable input allocations can be calculated from the estimated technology. A correct test for input nonjointness that discriminates between true and apparent jointness is derived in a framework that permits fully linear estimation of a second‐order flexible technology. To illustrate, these methods are applied to the Just‐Zilberman‐Hochman data set.