  This paper studies giant magnons in AdS_4 x CP^3 using both the string
sigma-model and the algebraic curve. We complete the dictionary of solutions by
finding the dyonic generalisation of the CP^1 string solution, which matches
the `small' giant magnon in the algebraic curve, and by pointing out that the
solution recently constructed by the dressing method is the `big' giant magnon.
We then use the curve to compute finite-J corrections to all cases, which for
the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we
recover the S^5 answer, but for the `small' and `big' giant magnons we obtain
new corrections.
