Over the past years, multi-parameter stacking has become a standard tool for seismic reflection data processing. Although several traveltime approximations for converted waves may be found in the literature, all of them are designed for a CMP-based observation geometry. In this paper we propose a double-square root traveltime approximation for converted waves from a curved interface. This approximation is appropriate for large offsets. In the special case of monotypic waves it gives comparable results with other multi-parameter moveout formulas. Furthermore, we demonstrate that a CRS-type traveltime approximation for converted waves may be derived from the new approximation. In this context, we also discuss a pragmatic search strategy. The key step of the strategy is the simulation of a zero-offset section by a stack of γ-CMP gathers, which may be considered as a first approximation of common conversion point gathers. For non-converted waves this approach transforms to the well-known pragmatic approach by Müller et al. (1998). The new operator does not require separation of PP and PS wavefields prior to stacking. In our examples, the effective wavefield attributes of converted and monotypic waves obtained by the corresponding type of the operator have comparable values and may be used in joint interpretation.