In traditional spin echo double resonance (SEDOR), the echo amplitude M is decreased when the observed spins S are flipped by pi together with the pi refocusing pulse on the observed spins I; the dependence on tau is then determined. In the new version of SEDOR, the echo amplitude is measured as a function of the S spin flip angle theta at a constant pulse spacing tau. The analysis is simple and powerful for long tau, where the strong collision limit applies. There, the variation of M with theta can be fit, yielding the number n of spins S to which each spin I is coupled. Data from amorphous silicon with 1H and 2D show the described effect. A MAS version of the new method is used on multiply labeled alanine and urea, with results in good agreement with the predictions for n = 2, as expected. By Fourier transforming M with respect to the flip angle theta, a stick spectrum results; the largest numbered non-vanishing stick yields the number n of spins S coupled to each spin I. Simulations are presented for an n = 2 system. The present technique is compared to the multiple-quantum spin-counting method. Copyright 1998 Academic Press.