  We present an analytic study of the phase diagram of the one-dimensional t-J
model and a couple of its cousins. To deal with the interactions induced by the
no double occupancy constraints, we introduce a deformation of the Hubbard
operators. When the deformation parameter $\Delta$ is small, the induced
interactions are softened, accessible by perturbation theory. We combine
bososnization with renormalization group techniques to map out the phase
diagram of the system. We argue that when $\Delta\to 1$, there is no essential
change in the phase diagram. Comparison with the existing results in the
literature obtained by other methods justifies our deformation approach.
