Abstract The method of Barrelet zeros has been used to study the ambiguities of our partial wave solutions for the reactions K −p→ Λπ 0 from 1550 to 2170 MeV. Details of this two-body analysis technique are presented and ambigous sets of partial waves corresponding to the same d σ/d ω and (d σ/d ω) P are analysed. Seven ambigous solutions have been found which maintain the dominant ∑ resonant structure [D3(1660), D5(1765), F5(1920), F7(2040)] but differ in the resonant couplings (t = Γ e Γ r /Γ ) for these states, as well as in the resonant structure in the lower partial waves. Evidence is given for the possible existence of new resonant states in the F5, D5 and F7 partial waves and for additional resonances in lower waves. The resonant structure suggested by the additional solutions is more prolific than the structure previously indicated for this reaction. Several solutions contain resonant “daughter” states at the same mass but with different J P in qualitative agreement with Veneziano models and suggestive of the Harari-Freund conjecture of purely resonant scattering in non-diffractive, inelastic channels. The ambiguities are experimentally distinguishable only by measurement of R and A, which are predicted from the solutions. Each solution has been shown to be consistent with semi-local duality from observed averaging about zero exhibited by Im A′( s, t), the invariant, t-channel helicity non-flip amplitude calculated at t = 0 and at t = m K ∗ 2 . Local averaging was not seen in B ( s, t), the t-channel helicity flip amplitude. The variation of resonant coupling among these solutions for the dominant resonances suggests that SU(3) tests involving the Λπ channel should be reconsidered. The results indicate that partial wave ambiguities should be more carefully studied and that the possible ∑ resonances should be looked for in other KN reactions.