  We construct two solutions of the minimally coupled Einstein-scalar field
equations, representing regular deformations of Schwarzschild black holes by a
self-interacting, static, scalar field. One solution features an exponentially
decaying scalar field and a triple-well interaction potential; the other one is
completely analytic and sprouts Coulomb-like scalar hair. Both evade the
no-hair theorem by having partially negative potential, in conflict with the
dominant energy condition. The linear perturbation theory around such
backgrounds is developed in general, and yields stability criteria in terms of
effective potentials for an analog Schr\"odinger problem. We can test for more
than half of the perturbation modes, and our solutions prove to be stable
against those.
