  We discuss the stability and masses of topological solitons in QCD and
strongly-interacting models of electroweak symmetry breaking with arbitrary
combinations of two inequivalent Lagrangian terms of fourth order in the field
spatial derivatives. We find stable solitons for only a restricted range of the
ratio of these combinations, in agreement with previous results, and we
calculate the corresponding soliton masses. In QCD, the experimental
constraints on the fourth-order terms force the soliton to resemble the
original Skyrmion solution. However, this is not necessarily the case in
strongly-interacting models of electroweak symmetry breaking, in which a
non-Skyrmion-like soliton is also possible. This possibility will be
constrained by future LHC measurements and dark matter experiments. Current
upper bounds on the electroweak soliton mass range between 18 and 59 TeV, which
would be reduced to 4.6 to 8.1 TeV with the likely sensitivity of LHC data to
the fourth-order electroweak Lagrangian parameters.
