This study compares three different therapies for treatment of refractory Pneumocystis carinii pneumonia (PCP) in patients with AIDS. "Refractory" means that the patient has failed to respond to at least 4 days of treatment with either of two standard therapies: (1) sulfamethoxazole/trimethoprim (SMX/TMP) or (2) pentamidine (PEN). This study compares therapy with trimetrexate (TMTX) and leucovorin (LCV) to standard therapy and standard therapy plus high-dose steroids (methylprednisolone). The purpose is to find better and safer forms of treatment for PCP in AIDS patients. There is at present no scientific information about the best treatment for an AIDS patient with PCP who is not improving while receiving the standard therapies (SMX/TMP or PEN). New drug treatments are available, including steroid therapy and TMTX, but there is no information proving that these new treatments work better than the standard therapies.