This article examines the relative performance of two commonly used methods of parameter estimation in factor analysis, maximum likelihood (ML) and ordinary least squares (OLS). It is shown that ML will sometimes fail to recover a known population factor structure when OLS succeeds. A simulation study was conducted in which two types of error (model and sampling error) were introduced separately and in combination into correlation matrices generated from known population structures with at least one relatively weak major domain factor. Simulated correlation matrices were factor analyzed using both ML and OLS, and recovery of the relatively weak factor(s) was assessed. In situations with a moderate amount of error, ML often failed to recover the weak factor while OLS succeeded. It is suggested that the correspondence between the assumptions inherent in each method regarding error and the actual nature of error in the data may affect the success of recovery of weak common factors. An example using empirical data is also presented.