Molecular shape is an important concept in drug design and virtual screening. Shape similarity typically uses either alignment methods, which dynamically optimize molecular poses with respect to the query molecular shape, or feature vector methods, which are computationally less demanding but less accurate.  The computational cost of alignment can be reduced by pre-aligning shapes, as is done with the Volumetric-Aligned Molecular Shapes (VAMS) method.  Here we introduce and evaluate Fragment Oriented Molecular Shapes (FOMS), where shapes are aligned based on molecular fragments.  FOMS enables the use of \textit{shape constraints}, a novel method for precisely specifying molecular shape queries that provides the ability to perform partial shape matching and supports search algorithms that function on an interactive time scale. When evaluated using the challenging Maximum Unbiased Validation dataset, shape constraints were able to extract significantly enriched subsets of compounds for the majority of targets, and FOMS matched or exceeded the performance of both VAMS and an optimizing alignment method of shape similarity search.