We report measurements of the resistive superconducting transitions of NbSe3 as a function of magnetic field for sufficient pressures to destroy the lower CDW. These indicate that NbSe3 is a bulk anisotropic superconductor with a total Meissner effect. The critical field anisotropies are well described by an effective mass model and the values obtained are in good agreement with those obtained by conductivity or Shubnikov-de Haas measurements. At ambient pressure we have measured zero-resistivity transitions for compacted samples, but do not find a total Meissner effect. Hence this superconductivity is not a bulk effect but is probably associated with barriers between domains in the sample.