  We calculate the microstates free entropy dimension of natural generators in
an amalgamated free product of certain von Neumann algebras, with amalgamation
over a hyperfinite subalgebra. In particular, some `exotic' Popa algebra
generators of free group factors are shown to have the expected free entropy
dimension. We also show that microstates and non--microstates free entropy
dimension agree for generating sets of many groups. In the appendix by Wolfgang
Lueck, the first L^2-Betti number for certain amalgamated free products of
groups is calculated.
