  A search for double beta decays of $^{110}$Pd and $^{102}$Pd into excited
states of the daughter nuclides has been performed using three ultra-low
background gamma-spectrometry measurements in the Felsenkeller laboratory,
Germany, the HADES laboratory, Belgium and at the LNGS, Italy. The combined
Bayesian analysis of the three measurements sets improved half-life limits for
the $2\nu\beta\beta$ and $0\nu\beta\beta$ decay modes of the $2^+_1$, $0^+_1$
and $2^+_2$ transitions in $^{110}$Pd to $2.9\cdot10^{20}$ yr,
$4.0\cdot10^{20}$ yr and $3.0\cdot10^{20}$ yr respectively and in $^{102}$Pd to
$7.6\cdot10^{18}$ yr, $8.8\cdot10^{18}$ yr and $1.4\cdot10^{19}$ yr
respectively with 90% credibility.
