Morphine, as I understand it, can cause a nasty reaction for some headache sufferers. And in general it's more used for acute treatment in emergency situations. Several other painkillers can be just as potent but safer and more effective. One of the strongest of those (again used in the worse situations) is a fentanyl patch.
DX: NDPH, Recovered CRPS
RX: Lamictal, Concerta (Methylphenidate), Clonazepam, Wellbutrin XL, Namenda, Oxycontin, Oxycodone, Melatonin, Magnesium supplements.
PRN: Ketamine nasal spray, Celebrex, Migranal, Haloperidol, Zyprexa, Lodine, Zofran, Phenergan, Thorazine, DHE IM, Droperidol IM, Toradol, Reglan, Ambien CR, Provigil, and all triptans