  In this paper we develop $L^{p}$ estimates for functions $u$ which are joint
quasimodes of semiclassical pseudodifferential operators $p_{1}(x,hD)$ and
$p_{2}(x,hD)$ whose characteristic sets meet with $k$th order contact,
$k\geq{}1$. As part of the technical development we use Fourier integral
operators to adapt a flat wavelet analysis to the curved level sets of
$p_{1}(x,\xi)$.
