  We present results of detailed study on the electron dispersions and Fermi
surface of lead telluride doped with $2\%$ of thallium, which is resonant
impurity in PbTe. Using the KKR--CPA method, Bloch spectral functions (BSFs),
which replace the dispersion relations in alloys, are calculated, and BSFs
intensity maps over the Brillouin zone (alloy Fermi surface cross-sections) are
presented. It is shown, that close to the valence band edge, Tl does not create
an isolated impurity band, but due to its resonant character, strongly disturbs
the host electronic bands, leading to disappearance of sharp and well defined
electronic energy bands. Consequences of this effect on the transport
properties are discussed and new qualitative explanation of the improvement in
thermoelectric properties of PbTe:Tl is suggested.
