We report precise mass and density measurements of two extremely hot sub-Neptune-size planets from the K2 mission using radial velocities, K2 photometry, and adaptive optics imaging. K2-66 harbors a close-in sub-Neptune-sized (2.49$^{+0.34}_{-0.24} R_oplus$) planet (K2-66b) with a mass of 21.3 $pm$ 3.6 $M_oplus$. Because the star is evolving up the sub-giant branch, K2-66b receives a high level of irradiation, roughly twice the main sequence value. K2-66b may reside within the so-called photoevaporation desert, a domain of planet size and incident flux that is almost completely devoid of planets. Its mass and radius imply that K2-66b has, at most, a meager envelope fraction (< 5%) and perhaps no envelope at all, making it one of the largest planets without a significant envelope. K2-106 hosts an ultra-short-period planet ($P$ = 13.7 hrs) that is one of the hottest sub-Neptune-size planets discovered to date. Its radius (1.82$^{+0.20}_{-0.14} R_oplus$) and mass (9.0 $pm$ 1.6 $M_oplus$) are consistent with a rocky composition, as are all other small ultra-short-period planets with well-measured masses. K2-106 also hosts a larger, longer-period planet (Rp = 2.77$^{+0.37}_{-0.23} R_oplus$, $P$ = 13.3 days) with a mass less than 24.4 $M_oplus$ at 99.7% confidence. K2-66b and K2-106b probe planetary physics in extreme radiation environments. Their high densities reflect the challenge of retaining a substantial gas envelope in such extreme environments.
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