We report on Doppler observations of three transiting planet candidates that were detected during Campaign 1 of the K2 mission. The Doppler observations were conducted with FIES, HARPS-N, and HARPS. We measure the mass of EPIC 201546283b, and provide constraints and upper limits for EPIC 201295312b and EPIC 201577035b. EPIC 201546283b is a warm Neptune orbiting its host star in 6.77 days and has a radius of {4.45}-0.33+0.33 {R}\oplus and a mass of {29.1}-7.4+7.5 {M}\oplus , which leads to a mean density of {1.80}-0.55+0.70 {{g}} {{cm}}-3. EPIC 201295312b is smaller than Neptune with an orbital period of 5.66 days, a radius of {2.75}-0.22+0.24 {R}\oplus , and we constrain the mass to be below 12 {M}\oplus at 95% confidence. We also find a long-term trend indicative of another body in the system. EPIC 201577035b, which was previously confirmed as the planet K2-10b, is smaller than Neptune, orbiting its host star in 19.3 days, with a radius of {3.84}-0.34+0.35 {R}\oplus . We determine its mass to be {27}-16+17 {M}\oplus , with a 95% confidence upper limit at 57 {M}\oplus , and a mean density of {2.6}-1.6+2.1 {\text{g cm}}-3. These measurements join the relatively small collection of planets smaller than Neptune with measurements or constraints of the mean density. Our code for performing K2 photometry and detecting planetary transits is now publicly available. Based on observations made with the NOT telescope under programme ID. 50-022/51-503 and 50-213(CAT), the TNG telescope under programme ID. AOT30.13, OPT15A_33, and CAT14B_121 and ESOs 3.6 m telescope at the La Silla Paranal Observatory under programme ID 095.C-0718(A).