  Recently, the Nancy Grace Roman Space Telescope (Roman) Project raised the
possibility of adding another filter to Roman. Based on the Filter Working
Group's recommendations, this filter may be a K-band filter, extending
significantly redder than the current-reddest F184. Among other scientific
possibilities, this K filter raises the possibility of measuring SNe Ia in the
rest-frame NIR out to higher redshifts than is possible with the current filter
complement. I perform a simple survey optimization for NIR SN Ia distances with
Roman, simultaneously optimizing both filter cutoffs and survey strategy. I
find that the roughly optimal K band extends from 19,000A--23,000A (giving
exposure times roughly half that of a 20,000A--23,000A Ks filter). Moving the K
much redder than this range dramatically increases the thermal background,
while moving the K band much bluer limits the redshift reach. Thus I find any
large modification reduces or eliminates the gain over the current F184. I
consider both rest-frame Y band and rest-frame J band surveys. Although the
proposed K band is too expensive for a large rest-frame Y band survey, it
increases the rest-frame J Figure of Merit by 59%.
