In many industrial situations, investigators will often begin an experimental study by employing a screening design to help them identify key factors for further investigation. Orthogonal main-effect plans (OMEP's) are often the screening designs of choice used in such situations. OMEP's allow for the estimation of all main effects of a factorial arrangement without correlation when the interactions are all assumed negligible. The problem of constructing OMEP's has been considered by a good many authors (for example, see Addelman 1962; Box and Hunter 1961; Chakrabarti 1956; Plackett 1946; Plackett and Burman 1946; Raghavarao 1971). When experimental runs are expensive, to minimize cost it is useful to know the minimal number of observations necessary to construct an OMEP for a given number of factors having a specified number of levels. In this article, I derive some sufficient conditions that can often be used to determine when an OMEP has a minimal number of observations. Methods of constructing OMEP's that satisfy the sufficient conditions obtained are also given.