  We study the entropy function of two N =2 string compactifications obtained
as freely acting orbifolds of N=4 theories : the STU model and the FHSV model.
The Gauss-Bonnet term for these compactifications is known precisely. We apply
the entropy function formalism including the contribution of this four
derivative term and evaluate the entropy of dyons to the first subleading order
in charges for these models. We then propose a partition function involving the
product of three Siegel modular forms of weight zero which reproduces the
degeneracy of dyonic black holes in the STU model to the first subleading order
in charges. The proposal is invariant under all the duality symmetries of the
STU model. For the FHSV model we write down an approximate partition function
involving a Siegel modular form of weight four which captures the entropy of
dyons in the FHSV model in the limit when electric charges are much larger than
magnetic charges.
