There is nothing wrong with centerpulls, as long as you can get replacement parts, such as that two-headed straddle cable. Nick and Noah are right: you need KoolStop pads, new cables, and new housings. I still have the original Weinmann Vainqueur 999 centerpulls on my Capo and wouldn't dream of replacing them. Likewise, I have a Mafac racer in front and a Peugeot-branded Weinmann 999 in back on my UO-8, and have no complaints about braking performance.
To boost your braking leverage by about 10 percent, replace your brake handles with the modern aero type.
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069