  Based on the shearlet transform we present a general construction of
continuous tight frames for $L^2(\mathbb{R}^2)$ from any sufficiently smooth
function with anisotropic moments. This includes for example compactly
supported systems, piecewise polynomial systems, or both. From our earlier
results it follows that these systems enjoy the same desirable approximation
properties for directional data as the previous bandlimited and very specific
constructions due to Kutyniok and Labate. We also show that the representation
formulas we derive are in a sense optimal for the shearlet transform.
