  We discuss constraints on which flat directions can have large vacuum
expectation values (VEVs) after inflation. We show that only flat directions
which are not charged under B-L and develop positive pressure due to
renormalization group effects can have large VEVs of order $\Mp$. For example,
within the MSSM only the $H_uH_d$ flat direction is found to be viable. This
strongly constrains the embedding of a broad class of inflationary models in
the MSSM or some other supersymmetric extension of the SM. For flat directions
with negative pressure, the condensate fragments into very large Q-balls which
we call Q-giants. We discuss the formation, evolution and reheating of these
Q-giants and show that they decay too late. The analysis requires taking into
account new phases of the flat directions, which have been overlooked in the
formation and dynamics of the Q-balls. These constraints may be ameliorated by
invoking a short period of thermal inflation. The latter, however, is viable in
a very narrow window of parameter space and requires fine tuning.
