Various smoothing procedures in stochastic transport leading to deterministic equations for the mean flux and its variance are presented, and the connections between them are discussed. Particular attention is paid to Volterra's functional calculus, which generates an algorithm, referred to as functional derivative algorithm (FDA), that produces deterministic equations describing the effects of stochasticity. These equations, which describe the effects of stochasticity to leading order, involve only the two-point correlation function of the spatial fluctuations. The utility of FDA is demonstrated by treating particular models of transport in unbounded media, and its general features are discussed in steady-state stochastic transport with suggestions for numerical solutions.