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We present an existence and stability theory for gravity-capillary solitarywaves with constant vorticity on the surface of a body of water of finitedepth. Exploiting a rotational version of the classical variational principle,we prove the existence of a minimiser of the wave energy $\mathcal H$ subjectto the constraint $\mathcal I=2\mu$, where $\mathcal I$ is the wave momentumand $0< \mu \ll 1$. Since $\mathcal H$ and $\mathcal I$ are both conservedquantities a standard argument asserts the stability of the set $D_\mu$ ofminimisers: solutions starting near $D_\mu$ remain close to $D_\mu$ in asuitably defined energy space over their interval of existence.  In the applied mathematics literature solitary water waves of the presentkind are described by solutions of a Korteweg-deVries equation (for strongsurface tension) or a nonlinear Schr\"{o}dinger equation (for weak surfacetension). We show that the waves detected by our variational method converge(after an appropriate rescaling) to solutions of the appropriate model equationas $\mu \downarrow 0$

Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity