  The distribution of the Fisher zeros in the Kallen-Lehmann approach to
three-dimensional Ising model is studied. It is argued that the presence of a
non-trivial angle (a cusp) in the distribution of zeros in the complex
temperatures plane near the physical singularity is realized through a strong
breaking of the 2D Ising self-duality. Remarkably, the realization of the cusp
in the Fisher distribution ultimately leads to an improvement of the results of
the Kallen-Lehmann ansatz. In fact, excellent agreement with Monte Carlo
predictions both at high and at low temperatures is observed. Besides,
agreement between both approaches is found for the predictions of the critical
exponent alpha and of the universal amplitude ratio Delta = A_+/A_-, within the
3.5% and 7% of the Monte Carlo predictions, respectively.
