The invention relates to peptides which contain N-methylated amino acid units and have improved water solubility. The invention also relates methods for treating a hormone-dependent tumor or a non-malignant indication that is treatable by LH-RH suppression, the method comprising administering to a patient in need of the treatment a therapeutically effective amount of a compound of the invention. Hormone-dependent cancers that can be treated with the methods of the invention include prostate cancer, breast cancer, ovarian cancer, endometrial cancer, and pancreatic cancer. Non-malignant indications which can be treated by the methods of the invention include benign prostate hyperplasia (BPH), endometriosis, acne, polycystic ovarian disease, dysmenorrhea, precocious puberty, and uterine fibroids and other leiomyomas.