A new, simplified theory for the analysis of the time-dependent development of the depth of scour at bridge contractions in cohesive soils under clear-water conditions is presented. The new theory is an extension of the clear-water scour theory for a long contraction currently used for noncohesive bed materials. It is based on the "scour rate in cohesive soils" concepts introduced recently by Briaud and his colleagues at Texas A&M University. A description of the simplifying assumptions made in the development of the theory and several applications with different bed soils and flow conditions are presented to illustrate the effects of various assumptions on the estimate of the scour depth. Limitations of the theory are also discussed. The results indicate that a very long time may be required in some cohesive soils for the scour depth to reach its maximum value for a given flow condition. The results also indicate that significant differences in the estimate of the scour depth may occur depending on the assumptions made about the behavior of the water surface elevation and the total head in the contraction during the development of the scour in the contraction.