Spoiled gradient echo sequences can only reach a homogeneous steady state if sufficiently strong crusher gradients are used in combination with RF phase cycling (RF spoiling). However, the signal depends quite sensitively on the chosen phase increment phi and-lacking analytical solutions-numerical simulations must be used to study the transient and steady-state magnetization. For the steady state an exact analytical solution is derived, which holds for arbitrary sequence and tissue parameters. Besides a considerably improved computation performance, the analytical approach enables a better understanding of the complicated dependence on phi. For short repetition times (TR) the regime of small phi turns out to be particularly interesting: It is shown that the typical phi(c), where RF spoiling starts to become effective, is essentially inversely proportional to T(2). This tissue dependence implies that contrasts can be considerably larger with partial spoiling (phi approximately phi(c)) than with conventional RF spoiling (phi >> phi(c)). As an example, the uptake of contrast agents in tissues is investigated. For typical parameters a considerably improved contrast enhancement can be obtained, both theoretically and experimentally.