Approximations of functional broadside tests maintain close-to-functional operation conditions in order to avoid overtesting of delay faults. Approximations were used earlier for increasing the fault coverage of functional broadside tests. This paper describes the first procedure that uses an approximation, referred to as piecewise-functional broadside tests, to achieve test compaction. Piecewise-functional broadside tests are characterized by a parameter p. A lower value of p indicates a closer proximity to functional operation conditions. The test compaction procedure combines a pair of tests, ti and tj, to form a test, ti,j, that can replace ti and tj without reducing the fault coverage, and thus reduce the number of tests. With ti and tj having parameter values pi and pj, respectively, the combined test ti,j has parameter value pi,j ≤ pi + pj. The procedure increases the bound p on pi,j gradually as it compacts the test set. Experimental results for benchmark circuits show that significant levels of test compaction can be achieved with p = 2. In addition, the procedure converges for a small value of p.