We consider the angular distribution of the diffracted intensity, I(q), for systems of disordered one-dimensional double-spaced islands with domain boundaries. Although I(q) is directly determined by the spatial pair correlations, it is often naturally reexpressed in terms of island size and separation distributions. We analyze the effect on I(q) of various approximate specifications of the island statistics. In particular, we highlight the approximations implicit in Guinier (-type) formulations, and provide a new very accurate approximation. Motivated by the scarcity of analysis for kinetically limited island growth (often seen in chemisorption), we consider such an irreversible cooperative filling model for which exact results are available for the (highly nontrivial) island statistics [and thus for I(q)]. We find that the (exact) integral-order beam intensity effectively disappears at saturation (where neighboring islands are out of phase) due to a propensity for cancellation of (a sum over) spatial pair correlations. This feature is missing not only in island-size-broadening-model (ISBM) calculations (which neglect the interisland interface), but also in Guinier formations. There is also significant interference at the half-order beams, and again Guinier formulations are inaccurate. Determination of average island size from these beam widths, via the usual ISBM algorithm, results in underestimation by a factor increasing to ∼3 as the coverage increases to saturation.