This article is an attempt to improve the efficiency of procedures for compositional synthesis of design solutions using building blocks. These procedures have found use in a wide range of applications, and are one of the most substantial outcomes of research into automated synthesis of design solutions. Due to their combinatorial nature, these procedures are highly inefficient in solving problems, especially when the database of building blocks for synthesis or the problem size is large. Previous literature often focuses on improving only the algorithm part of a procedure, although it is both its algorithm and database which together determine the overall efficiency of the procedure. This article reports the construction and analysis of an improved algorithm, based on bidirectional search, for efficient compositional synthesis of design solutions using a set of building blocks.