  Inelastic light (Raman) scattering has been used to study electronic
excitations and phonon anomalies in detwinned, slightly overdoped
YBa$_2$Cu$_3$O$_{6.95}$ and moderately overdoped
Y$_{0.85}$Ca$_{0.15}$Ba$_2$Cu$_3$O$_{6.95}$ single crystals. In both samples
modifications of the electronic pair-breaking peaks when interchanging the a-
and b-axis were observed. The lineshapes of several phonon modes involving
plane and apical oxygen vibrations exhibit pronounced anisotropies with respect
to the incident and scattered light field configurations. Based on a
theoretical model that takes both electronic and phononic contributions to the
Raman spectra into account, we attribute the anisotropy of the
superconductivity-induced changes in the phonon lineshapes to a small s-wave
admixture to the $d_{x^2-y^2}$ pair wave-function. Our theory allows us to
disentangle the electronic Raman signal from the phononic part and to identify
corresponding interference terms. We argue that the Raman spectra are
consistent with an s-wave admixture with an upper limit of 20 percent.
