  We generate an explicit four-fold infinity of physically acceptable exact
perfect fluid solutions of Einstein's equations by way of conformal
transformations of physically unacceptable solutions (one way to view the use
of isotropic coordinates). Special cases include the Schwarzschild interior
solution and the Einstein static universe. The process we consider involves
solving two equations of the Riccati type coupled by a single generating
function rather than a specification of one of the two metric functions.
