  We present experimental results from a new scheme for magneto-optically
trapping strontium monofluoride (SrF) molecules, which provides increased
confinement compared to our original work. The improved trap employs a new
approach to magneto-optical trapping presented by M. Tarbutt, \emph{arXiv
preprint} 1409.0244, which provided insight for the first time into the source
of the restoring force in magneto-optical traps (MOTs) where the cycling
transition includes dark Zeeman sublevels (known as type-II MOTs). We measure a
radial spring constant $20\times$ greater than in our original work with SrF,
comparable to the spring constants reported in atomic type-II MOTs. We achieve
a trap lifetime $\tau_{\rm{MOT}}=136(2)$~ms, over $2\times$ longer than
originally reported for SrF. Finally, we demonstrate further cooling of the
trapped molecules by briefly increasing the trapping lasers' detunings. Our
trapping scheme remains a straightforward extension of atomic techniques and
marks a step towards the direct production of large, dense, ultracold molecular
gases via laser cooling.
