  We perform a general analysis of the R-parity conserving dimension-five
operators that can be present beyond the Minimal Supersymmetric Standard Model.
Not all these operators are actually independent. We present a method which
employs spurion-dependent field redefinitions that removes this "redundancy"
and establishes the minimal, irreducible set of these dimension-five operators.
Their potential effects on the MSSM Higgs sector are discussed to show that the
tree level bound $m_h\leq m_Z$ cannot be easily lifted within the
approximations used, and quantum corrections are still needed to satisfy the
LEPII bound. An ansatz is provided for the structure of the remaining couplings
in the irreducible set of D=5 operators, which avoids phenomenological
constraints from flavor changing neutral currents. The minimal set of operators
brings new couplings in the effective Lagrangian, notably "wrong"-Higgs Yukawa
couplings and contact fermion-fermion-scalar-scalar interactions, whose effects
are expected to be larger than those generated in the MSSM at loop or even tree
level. This has implications in particular for LHC searches for supersymmetry
by direct squark production.
