  A connected matching in a graph $G$ is a matching contained in a connected
component of $G$. A well-known method due to {\L}uczak reduces problems about
monochromatic paths and cycles in complete graphs to problems about
monochromatic connected matchings in almost complete graphs. We show that these
can be further reduced to problems about monochromatic connected matchings in
complete graphs.
  We illustrate the potential of this new reduction by showing how it can be
used to determine the $3$-colour Ramsey number of long paths, using a simpler
argument than the original one by Gy\'arf\'as, Ruszink\'o, S\'ark\"ozy, and
Szemer\'edi (2007).
