  We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving
an improvement to the non-archimedean Second Main Theorems of Ru and An in the
case where all the hypersurfaces have degree greater than one and all
intersections are transverse. In particular, under a transversality assumption,
if f is a nonconstant non-archimedean analytic map to P^n and D_1,..,D_q are
hypersurfaces of degree d, we prove the defect relation
\sum_{i=1}^q\delta_f(D_i)\leq n-1+1/d, which is sharp for all positive integers
n and d.
