Local structural correlations and small-angle scattering profiles are studied using the polymer reference interaction site model (PRISM) integral equation theory for a series of structurally asymmetric diblock copolymer melts in the athermal limit. Motivated by recent experimental work on polyolefin and polydiene copolymers, we have chosen the block. aspect ratios and the overall degree of copolymer asymmetry to be representative of those systems. The extent of nonrandom mixing in the fluid is quantified by calculating length scale dependent "effective compositions". These deviations from the bulk composition in the athermal fluid are compared to those of a fully interacting thermal system. The athermal contribution to nonrandom mixing, resulting from pure stiffness asymmetry, is quite small relative to the effects brought on by unfavorable enthalpic AB interactions. Nonetheless, deviations from random mixing in the athermal limit can lead to appreciable unfavorable enthalpic interactions between components within a thermodynamic perturbative scheme. Large departures from the widely assumed equality of the three partial collective structure factors are also found, suggesting that the extraction of a single chi parameter by fitting to a form which assumes incompressibility may in some cases be unreliable.