We show that if actions more general than the usual simple plaquette action (\ensuremath{\sim}${\mathit{F}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}^{2}$) are considered, then compact U(1) pure gauge theory in three Euclidean dimensions can have two phases. Both phases are confining phases; however, in one phase the monopole condensate spontaneously ``magnetizes.'' For a certain range of parameters the phase transition is continuous, allowing the definition of a strong coupling continuum limit. We note that these observations have relevance to the ``fictitious'' gauge field theories of strongly correlated electron systems, such as those describing high-${\mathit{T}}_{\mathit{c}}$ superconductors. \textcopyright{} 1996 The American Physical Society.