  In the following we are interested in the spectral gaps of discrete
quasiperiodic Schr\"odinger operators when the frequency is Diophantine, the
potential is analytic, and in the subcritical regime. The gap-labelling theorem
asserts in this context that each gap has constant rotation number, labeled by
some integer. We prove that the size of these gaps decays exponentially fast
with respect to their label. This refines a subexponential bound obtained
previously by Sana Ben Hadj Amor. Contrary to her approach, which is based on
KAM methods, the arguments in the present paper are non-perturbative, and use
quantitative reducibility estimates obtained by Artur Avila and Svetlana
Jitomirskaya. As a corollary of our result, we show that under the previous
assumptions, the spectrum is 1/2-homogeneous.
