  We investigate the profile of random P\'olya trees of size $n$ when only
nodes of degree $d$ are counted in each level. It is shown that, as in the case
where all nodes contribute to the profile, the suitably normalized profile
process converges weakly to a Brownian excursion local time. Moreover, we
investigate the joint distribution of the number of nodes of degree $d_1$ and
$d_2$ in the levels of the tree.
