  We analyse the $p p \to p \Lambda K^+$ total cross section data which were
recently measured by the COSY-11 collaboration at an energy 2~MeV above the
reaction threshold. Our analysis suggests that the measurement of the invariant
mass spectrum for the $\Lambda K^+$ at energies around 100 MeV above the
threshold can provide a new constraint on the theoretical calculations for this
reaction. In particular, the measurement can give a clue as to whether the
reaction is dominated by resonance excitation or not. Thus, it should
contribute to further understanding of the strangeness production mechanism. We
show the invariant mass spectra for the $\Lambda K^+$ system in these optimal
kinematic conditions calculated by several approaches, and demonstrate that our
suggestion is experimentally feasible.
