We present astrometric parallaxes for 18 suspected nearby stars selected from the LSPM-north proper motion catalog. Sixteen objects are confirmed to be main sequence M dwarfs within 16 parsecs of the Sun, including three stars (LSPM J0011+5908, LSPM J0330+5413, LSPM J0510+2714) which lie just within the 10 parsec horizon. Two other targets (LSPM J1817+1328, LSPM J2325+1403) are confirmed to be nearby white dwarfs at distances of 14 and 22 parsecs, respectively. One of our targets, the common proper motion pair LSPM J0405+7116E + LSPM J0405+7116W, is revealed to be a triple system, with the western component resolved into a pair of 16th magnitude stars (LSPM J0405+7116W-A and LSPM J0405+7116W-B) with a 0.7±0.1 ′′ angular separation. We find two stars (LSPM J1314+1320 and LSPM J1757+7042) to be significantly overluminous for their colors, and conclude that these may be unresolved doubles/multiples.