The classic common-midpoint (CMP) stack, which sums along offsets, suffers in challenging environments in which the acquisition is sparse. In the past, several multiparameter stacking techniques were introduced that incorporate many neighboring CMPs during summation. This increases data redundancy and reduces noise. Multiparameter methods that can be parameterized by the same wavefront attributes are multifocusing (MF), the common-reflection-surface (CRS), implicit CRS, and nonhyperbolic CRS (nCRS). The CRS-type operators use a velocity-shift mechanism to account for heterogeneity by changing the slope of the asymptote. On the other hand, MF uses a different mechanism: a shift of reference time while preserving the slope of the asymptote. We have formulated MF such that it uses the same mechanism as the CRS-type operators and compare them on a marine data set. In turn, we investigate the behavior of time-shifted versions of the CRS-type approximations. To provide a fair comparison, we use a global optimization technique, differential evolution, which allows to accurately estimate a solution without an initial guess solution. Our results indicate that the velocity-shift mechanism performs, in general, better than the one incorporating a time shift. The double-square-root operators are also less sensitive to the choice of aperture. They perform better in the case of diffractions than conventional hyperbolic CRS, and this fact is in good agreement with previous works. In our work the nCRS is of almost the same computational cost as that of conventional hyperbolic CRS, but it generally leads to a superior fit; therefore, we recommend its use in the future.