We present a new type of soliton, found in models characterized by opposing dispersions and competing nonlinearities at fundamental and second harmonics. They are isolated solitary waves, existing at discrete values of the propagation constant inside the system’s continuous spectrum. We show analytically, and verify by simulations, that the fundamental solitons are linearly stable. They can be nonlinearly stable or unstable, depending on the sign of the energy perturbation, which could make these pulses useful for switching applications. Higher-order solitons are found, too, but they are linearly unstable.