  We show that a free product of a II_1-factor and a finite von Neumann algebra
with amalgamation over a finite dimensional subalgebra is always a II_1-factor,
and provide an algorithm for describing it in terms of free products (with
amalgamation over the scalars) and compression/dilation. As an application, we
show that the class of direct sums of finitely many von Neumann algebras that
are interpolated free group factors, hyperfinite II_1-factors, type I_n
algebras for n finite, and finite dimensional algebras, is closed under taking
free products with amalgamation over finite dimensional subalgebras.
