  We study classical and quantum finite-size corrections to giant magnons in
AdS_4 x CP^3 using generalised L\"uscher formulae. L\"uscher F-terms are
organised in powers of the exponential suppression factor exp(-Delta/2h)^m, and
we calculate all terms in this series, matching one-loop algebraic curve
results from our previous paper arXiv:1006.2174. Starting with the second term,
the structure of these terms is different to those in AdS_5 x S^5 thanks to the
appearance of heavy modes in the loop, which can here be interpreted as
two-particle bound states in the mirror theory. By contrast, physical bound
states can represent dyonic giant magnons, and we also calculate F-terms for
these solutions. L\"uscher mu-terms, suppressed by exp(-Delta/E), instead give
at leading order the classical finite-size correction. For an elementary dyonic
giant magnon, we recover the correction given by arXiv:0903.3365. We then
extend this to calculate the next term in 1/h, giving a one-loop prediction.
Finally we also calculate F-terms for the various composite giant magnons, RP^3
and `big', again finding agreement to all orders.
