A putter-head (1) has its center of mass (15) spaced p mm behind its impact-face (8) at a height h_c mm above the head-bottom (9), a loft angle ₁₂ at height 12 mm above the head-bottom (9), a moment of inertia/kg-mm² about the vertical axis through the center of mass (15), a mass M kg and a radius of gyration of K mm about the heel-toe axis (2-10) of the head through the center of mass (15), where p/l is not more than 0.18, h_c is less than [12-psin(₁₂)], and a parameter G=[p+(3.2+70M)K²/p] is less than 350. The ratio d₂/K is less than 1.0, d₂ mm being the vertical offset above the heel-toe axis (2-10) of the axis of attachment of the putter-shaft (3) to the putter-head (1); the attachment-axis of the shaft may be spaced by no more than the shaft-radius from the center of mass. The impact-face (36) may have an upper flat section (38) that merges smoothly into a cylindrical lower section (39), and the head (30) may be constructed with a high-density part (32;40) that extend lengthwise of the heel-toe axis and is either bonded to the underside of a lower-density part (31), or forms both an upstanding front flange (43) and a rear body-section (41) of larger mass than, and spaced from, the flange (43).