A sampling plan that produces minimal sample variance is optimal. If a sediment is homogeneous for a particular character, a plan using random samples is adequate; if unlike elements are found in nonrandom aggregations, however, other forms of sampling are more efficient. An outcrop of the Pendleton Formation at Grand Ecore Bluff, La., was subdivided into five gross units; two random samples from each unit were thin sectioned perpendicular to the bedding. In grain size analysis, the layers in three-layered thin sections were treated as individual units of rank equal to the seven homogeneous sections. The analysis showed that the units carrying minimal variance are the homogeneous units within thin sections.