  Single-energy partial-wave analysis has often been applied as a way to fit
data with minimal model dependence. However, remaining unconstrained, partial
waves at neighboring energies will vary discontinuously because the overall
amplitude phase cannot be determined through single-channel measurements. This
problem can be mitigated through the use of a constraining penalty function
based on an associated energy-dependent fit. However, the weight given to this
constraint results in a biased fit to the data. In this paper, for the first
time, we explore a constraining function which does not influence the fit to
data. The constraint comes from the overall phase found in multi-channel fits
which, in the present study, are the Bonn-Gatchina and J\"ulich-Bonn
multi-channel analyses. The data are well reproduced and weighting of the
penalty function does not influence the result. The method is applied to $K
\Lambda$ photoproduction data and all observables can be maximally well
reproduced. While the employed multi-channel analyses display very different
multipole amplitudes, we show that the major difference between two sets of
multipoles can be related to the different overall phases.
