Context. Multiplanet systems are excellent laboratories to test planet formation models as all planets are formed under the same initial conditions. In this context, systems transiting bright stars can play a key role, since planetary masses, radii, and bulk densities can be measured. Aims. GJ 9827 (K2-135) has recently been found to host a tightly packed system consisting of three transiting small planets whose orbital periods of 1.2, 3.6, and 6.2 days are near the 1:3:5 ratio. GJ 9827 hosts the nearest planetary system (~30 pc) detected by NASA’s Kepler or K2 space mission. Its brightness (V = 10.35 mag) makes the star an ideal target for detailed studies of the properties of its planets. Methods. Combining the K2 photometry with high-precision radial-velocity measurements gathered with the FIES, HARPS, and HARPS-N spectrographs we revised the system parameters and derive the masses of the three planets. Results. We find that GJ 9827 b has a mass of M_b = 3.69_−0.46^+0.48 M_⊕ and a radius of R_b = 1.58_−0.13^+0.14 R_⊕, yielding a mean density of ρ_b = 5.11_−1.27^+1.74 g cm⁻³. GJ 9827 c has a mass of M_c = 1.45_−0.57^+0.58 M_⊕, radius of R_c = 1.24_−0.11^+0.11 R_⊕, and a mean density of ρ_c = 4.13_−1.77^+2.31 g cm⁻³. For GJ 9827 d, we derive M_d = 1.45_−0.57^+0.58 M_⊕, R_d = 1.24_−0.11^+0.11 R_⊕, and ρ_d = 1.51_−0.53^+0.71 g cm⁻³. Conclusions. GJ 9827 is one of the few known transiting planetary systems for which the masses of all planets have been determined with a precision better than 30%. This system is particularly interesting because all three planets are close to the limit between super-Earths and sub-Neptunes. The planetary bulk compositions are compatible with a scenario where all three planets formed with similar core and atmosphere compositions, and we speculate that while GJ 9827 b and GJ 9827 c lost their atmospheric envelopes, GJ 9827 d maintained its primordial atmosphere, owing to the much lower stellarirradiation. This makes GJ 9827 one of the very few systems where the dynamical evolution and the atmosphericescape can be studied in detail for all planets, helping us to understand how compact systems form and evolve.