  We present a systematic determination of the order hbar fermionic energy
shift when an electroweak string is perturbed. We show that the combined effect
of zero modes, bound states and continuum states is to lower the total
fermionic ground state energy of the string when the Higgs instability of the
string is excited. The effect of the Dirac sea is thus to destabilise the
string. However, this effect can be offset by populating positive energy
states. Fermions enhance the stability of an electroweak string with
sufficiently populated fermionic bound states.
