  We present the discovery and phase-coherent timing of four highly dispersed
millisecond pulsars (MSPs) from the Arecibo PALFA Galactic plane survey: PSRs
J1844+0115, J1850+0124, J1900+0308, and J1944+2236. Three of the four pulsars
are in binary systems with low-mass companions, which are most likely white
dwarfs, and which have orbital periods on the order of days. The fourth pulsar
is isolated. All four pulsars have large dispersion measures (DM > 100 pc
cm-3), are distant (> 3.4 kpc), faint at 1.4 GHz (< 0.2 mJy), and are fully
recycled (with spin periods P between 3.5 and 4.9 ms). The three binaries also
have very small orbital eccentricities, as expected for tidally circularized,
fully recycled systems with low-mass companions. These four pulsars have DM/P
ratios that are among the highest values for field MSPs in the Galaxy. These
discoveries bring the total number of confirmed MSPs from the PALFA survey to
fifteen. The discovery of these MSPs illustrates the power of PALFA for finding
weak, distant MSPs at low-Galactic latitudes. This is important for accurate
estimates of the Galactic MSP population and for the number of MSPs that the
Square Kilometer Array can be expected to detect.
