  We calculate the ground state energies of closed k-strings in
(2+1)-dimensional SU(N) gauge theories, for N=4,5,6,8 and k=2,3,4. From the
dependence of the ground state energy on the string length, we infer that such
k-strings are described by an effective string theory that is in the same
bosonic universality class (Nambu-Goto) as the fundamental string. When we
compare the continuum k-string tensions to the corresponding fundamental string
tensions, we find that the ratios are close to, but typically 1-2 percent
above, the Casimir scaling values favoured by some theoretical approaches.
Fitting the N-dependence in a model-independent way favours an expansion in 1/N
(as in Casimir scaling) rather than the 1/N^2 that is suggested by naive colour
counting. We also observe that the low-lying spectrum of k-string states falls
into sectors that belong to particular irreducible representations of SU(N),
demonstrating that the dynamics of string binding knows about the full gauge
group and not just about its centre.
