  We systematically construct a class of two-dimensional $(2,2)$ supersymmetric
gauged linear sigma models with phases in which a continuous subgroup of the
gauge group is totally unbroken. We study some of their properties by employing
a recently developed technique. The focus of the present work is on models with
one K\"ahler parameter. The models include those corresponding to Calabi-Yau
threefolds, extending three examples found earlier by a few more, as well as
Calabi-Yau manifolds of other dimensions and non-Calabi-Yau manifolds. The
construction leads to predictions of equivalences of D-brane categories,
systematically extending earlier examples. There is another type of surprise.
Two distinct superconformal field theories corresponding to Calabi-Yau
threefolds with different Hodge numbers, $h^{2,1}=23$ versus $h^{2,1}=59$, have
exactly the same quantum K\"ahler moduli space. The strong-weak duality plays a
crucial r\^ole in confirming this, and also is useful in the actual computation
of the metric on the moduli space.
