We investigate whether the subhaloes of Lambda cold dark matter (ΛCDM) galaxy haloes have potentials consistent with the observed properties of Milky Way satellites, particularly those with high-quality photometric and kinematic data: Fornax, Leo I, Sculptor, Sextans and Carina. We compare spherical models with isotropic velocity dispersion tensors to the observed, circularly averaged star counts, line-of-sight velocity dispersion profiles and line-of-sight velocity distributions. We identify subhaloes within the six high-resolution dark matter haloes of the Aquarius Project for which the spherically averaged potentials result in excellent fits to each of the five galaxies. In particular, our simple one-integral models reproduce the observations in the inner regions, proving that these data are fully consistent with ΛCDM expectations and do not require cored dark matter distributions. For four of the five satellites the fits require moderately cusped stellar density profiles. The star count data for Leo I, however, do require a cored distribution of star counts. Current data suggest that these five satellites may be hosted by ΛCDM subhaloes with maximum circular velocities in the range 10–30 km s−1.