or a derivation of a sufficiently stringent upper limit on $m_1$ (or $\Sigma$). It was also pointed out in [@PPW] that the possibility of finding CP-violation “requires quite accurate measurements” of and, say, of $m_{\bar{\nu}_e}$, “and holds only for a limited range of values of the relevant parameters”. The aim of the present paper is to quantify these requirements, and to better determine the ranges of values of the parameters in question, which could allow to detect CP-violation due to the Majorana CP-violating phases. We discuss also the requirement the possibility of establishing CP-violation imposes on the uncertainty in the values of the -decay nuclear matrix elements. Let us add that at present no viable alternative to the measurement of for getting information about the Majorana CP-violating phases $\alpha_{21}$ and $\alpha_{31}$ exists (see, e.g., [@WRJPhys]), or can be foreseen to exist in the next $\sim 8$ years.

The problem of detecting CP-violation associated with Majorana neutrinos by measuring ${\mbox{$\left|  < \! m  \! > \right| \ $}}$ and $m_{\bar{\nu}_e}$ (or $\Sigma$) was discussed recently also in ref. [@BargerSNO2bb]. The authors of [@BargerSNO2bb], after making a certain number of assumptions about the experimental and theoretical developments in the field of interest 