1. A multi-piece solid golf ball comprising a core of at least one layer, a cover of at least one layer, and at least one intermediate layer interposed between the core and the cover, wherein the core has a deflection when compressed under a final load of 1,275 N (130 kgf) from an initial load state of 98 N (10 kgf) of at least 4.0 mm, the intermediate layer material has a melt flow rate (MFR) of at least 2.5 g/10 min, the intermediate layer has a thickness of from 1.0 to 1.8 mm, the cover is composed primarily of polyurethane, the cover has a thickness of from 0.5 to 1.0 mm, the cover has a Shore D hardness of at least 55, the sum of the intermediate layer thickness and the cover thickness is not more than 2.2 mm, and the value obtained by subtracting the Shore D hardness of the intermediate layer material from the Shore D hardness of the cover material is from ?10 to 0, andwherein the core is formed of a rubber composition comprising:
(a) a base rubber,
(b) an ?,?-unsaturated carboxylic acid and/or a metal salt thereof,
(c) a crosslinking initiator, and
(d) a metal carboxylate in which the carboxylic acid bonded to metal is of two or more different types and at least one of the carboxylic acids has 8 or more carbon atoms, the component (d) being selected from the group consisting of zinc monostearate monopalmitate, zinc monostearate monomyristate, zinc monostearate monolaurate, zinc monopalmitate monomyristate, zinc monopalmitate monolaurate, zinc monostearate monoacrylate, zinc monostearate monomethacrylate, zinc monostearate monomaleate, zinc monostearate monofumarate, zinc monopalmitate monoacrylate, zinc monopalmitate monomethacrylate, zinc monopalmitate monomaleate, zinc monopalmitate monofumarate, zinc monomyristate monoacrylate, zinc monomyristate monomethacrylate, zinc monomyristate monomaleate, zinc monomyristate monofumarate, zinc monolaurate monoacrylate, zinc monolaurate monomethacrylate, zinc monolaurate monomaleate and zinc monolaurate monofumarate.