This paper describes a new class of nonsymmetric maximally flat lowpass FIR filters. By subjecting the magnitude and group delay responses (individually) to differing numbers of flatness constraints, the new filters are obtained. It is found that these filters achieve a smaller delay than symmetric filters while maintaining relatively constant group delay around w=0, with no degradation of the frequency response magnitude. The design of these filters is initially investigated using Groebner bases. An analytic design technique, applicable to a subset of the forgoing filters, is provided that does not depend on Groebner basis computations.