  It has recently been demonstrated with Monte Carlo studies that combining the
well-known Y-splitter and trimming techniques gives rise to important gains in
the signal significance achievable for boosted electroweak boson tagging at
high $p_t$. Here we carry out analytical calculations that explain these
findings from first principles of QCD both for grooming via trimming and via
the modified mass-drop tagger (mMDT). We also suggest modifications to
Y-splitter itself, which result in great simplifications to the analytical
results both for pure Y-splitter as well as its combination with general
grooming methods. The modifications also lead to further performance gains,
while making the results largely independent of choice of groomer. We discuss
the implications of these findings in the broader context of optimal methods
for boosted object studies at hadron colliders.
