We present a new set of supersymmetric stationary solutions of pure N
= 4, d = 4 supergravity (and, hence, of low-energy effective string th
eory) that generalize (and include) the Israel-Wilson-Pejes solutions
of Einstein-Maxwell theory. All solutions have 1/4 of the supersymmetr
ies unbroken and some have 1/2. The full solution is determined by two
arbitrary complex harmonic functions H-1,H-2 which transform as a dou
blet under SL(2,R) S duality and N complex constants k((n)) that trans
form as an SO(N) vector. This set of solutions is, then, manifestly du
ality invariant. When the harmonic functions are chosen to have only o
ne pole, all the general resulting point-like objects have supersymmet
ric rotating asymptotically Taub-NUT metrics with 1/2 or 1/4 of the su
persymmetries unbroken. The static, asymptotically Bat metrics describ
e supersymmetric extreme black holes. Only those breaking 3/4 of the s
upersymmetries have regular horizons. The stationary asymptotically fl
at metrics do not describe black holes when the angular momentum does
not vanish, even in the case in which 3/4 of the supersymmetries are b
roken.