  In this paper we study the number $r_{bwt}$ of equal-letter runs produced by
the Burrows-Wheeler transform ($BWT$) when it is applied to purely morphic
finite words, which are words generated by iterating prolongable morphisms.
Such a parameter $r_{bwt}$ is very significant since it provides a measure of
the performances of the $BWT$, in terms of both compressibility and indexing.
In particular, we prove that, when $BWT$ is applied to any purely morphic
finite word on a binary alphabet, $r_{bwt}$ is $\mathcal{O}(\log n)$, where $n$
is the length of the word. Moreover, we prove that $r_{bwt}$ is $\Theta(\log
n)$ for the binary words generated by a large class of prolongable binary
morphisms. These bounds are proved by providing some new structural properties
of the \emph{bispecial circular factors} of such words.
