An orthogonal, refinable, scaling vector can generate a multiresolution $\{ V_j \}_{j \in \textbf{Z}}$ that is uniform in the sense that the knot sequence associated with $V_0$ is uniformly spaced (shift-invariant uniformity) and the knot sequence associated with $V_{j+1}$ is a dyadic refinement of the knot sequence associated with $V_j$ (scale-invariant uniformity). A semi-regular multiresolution is one which possesses scale-invariant uniformity, but the knot sequence associated with $V_0$ is an arbitrary, non-uniform knot sequence. In this talk, a procedure is given for generating such a semi-regular multiresolution from an orthogonal, refinable scaling vector that is minimally supported, that is, one that is supported on [-1,1] and satisfies a particular local linear independence property. The procedure results in a semi-regular multiresolution with the same smoothness and polynomial reproduction as in the uniform case. Examples of semi-regular scaling vectors and multiwavelets will be given.