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The determination of the earth's gravity field from satellite gravity gradiometry is an inverse or ill-posed problem requiring regularization. In geodesy the regularization is usually done by adding a priori information, Kaula's rule for example. This can be interpreted as constraining the signal. In the present study satellite gravity gradiometry measurements are considered so one could also imagine to constrain the second derivatives of the gravity potential. The aim here is to compare the regularization by constraining the signal itself to regularization by constraining the second derivatives. This is done for several gradiometric mission scenarios. The comparison is based on the mean square error of the solutions, which is the sum of the propagated error and the, often neglected, regularization error. The total error of the solutions is computed and the errors are propagated to geoid heights as well. The main conclusions are that the signal constraint is more satisfactory than the second derivative constraint, that the regularization error is not negligible and that additional measurements or other solution methods are needed.