Recent research has shown that effective jammer and clutter suppression is best performed with fully space-time adaptive processing. However, allowing adaptive weights on every tap on every element is computationally prohibitive and requires too many samples to converge. Eigenvalue analysis shows that the required number of degrees of freedom (DOF) is significantly less than the dimensionality of the space-time data (i.e. the total # of DOF's). Therefore it should not be necessary to use adaptive weights on every tap of every element. The objective then becomes to reduce the number of DOF's (=adaptive weights) used for interference suppression. We propose a general and fundamental two-dimensional subband decomposition approach which optimally (in terms of canceler mean squared error) chooses the desired number of DOF's using an easily computed criterion. Each adaptive weight operates on a linear combination of sensor and tap data, rather than a subset of sensors and taps. M degrees of freedom corresponds to M linear combinations. Furthermore, these linear combinations are formed in a data-dependent but easily computed way, so that the DOF's can change as the interference changes.