  Let p be a fibration over a finite simplicial complex, whose fibers have the
homotopy type of finite simplicial complexes. Then p is equivalent to an
approximate fibration whose total space is a compact ENR. The proof uses
homotopy coherent diagrams and their homotopy colimits. We also comment on the
simple homotopy type of the total space and give an application to the fibering
of Hilbert cube manifolds.
