  We prove a strong conditional unique continuation estimate for irreducible
quasimodes in rotationally invariant neighbourhoods on compact surfaces of
revolution. The estimate states that Laplace quasimodes which cannot be
decomposed as a sum of other quasimodes have $L^2$ mass bounded below by
$C_\epsilon \lambda^{-1 - \epsilon}$ for any $\epsilon>0$ on any open
rotationally invariant neighbourhood which meets the semiclassical wavefront
set of the quasimode. For an analytic manifold, we conclude the same estimate
with a lower bound of $C_\delta \lambda^{-1 + \delta}$ for some fixed
$\delta>0$.
