  Context. CEMP-no stars are long-lived low-mass stars with a very low iron
content, overabundances of carbon and no or minor signs for the presence of s-
or r-elements. Although their origin is still a matter of debate, they are
often considered as being made of a material ejected by a previous stellar
generation (source stars). Aims. We place constraints on the source stars from
the observed abundance data of CEMP-no stars. Methods. We computed source star
models of 20, 32, and 60 M$_{\odot}$ at Z = 10$^{-5}$ with and without fast
rotation. For each model we also computed a case with a late mixing event
occurring between the hydrogen and helium-burning shell $\sim$ 200 yr before
the end of the evolution. This creates a partially CNO-processed zone in the
source star. We use the 12C/13C and C/N ratios observed on CEMP-no stars to put
constraints on the possible source stars (mass, late mixing or not). Then, we
inspect more closely the abundance data of six CEMP-no stars and select their
preferred source star(s). Results. Four out of the six CEMP-no stars studied
cannot be explained without the late mixing process in the source star. Two of
them show nucleosynthetic signatures of a progressive mixing (due e.g. to
rotation) in the source star. We also show that a 20 M$_{\odot}$ source star is
preferred compared to one of 60 M$_{\odot}$ and that likely only the outer
layers of the source stars were expelled to reproduce the observed 12C/13C.
Conclusions. The results suggest that (1) a late mixing process could operate
in some source stars, (2) a progressive mixing, possibly achieved by fast
rotation, is at work in several source stars, (3) $\sim$ 20 M$_{\odot}$ source
stars are preferred compared to $\sim$ 60 M$_{\odot}$ ones, and (4) the source
star might have preferentially experienced a low energetic supernova with large
fallback.
