We report BT/(RI)(C) data for a select group of 14 Cepheids in the Lar
ge Magellanic Cloud and eight in the Small Magellanic Cloud that have
preexisting radial velocity curves. The photometry was obtained as par
t of a program to determine distances to these Cepheids by means of th
e visual surface brightness technique and to improve significantly the
optical BV(RI)(C) light curves of Magellanic Cloud Cepheids. The data
were acquired on the 0.9 m telescope at Cerro Tololo Inter-American O
bservatory with the CFCCD instrument and with the 1 m photometric tele
scope at ESO using aperture photometry. The median number of measures
per Cepheid is 46 in each band, and the uncertainty in the photometry
is typically +/-0.01 mag. Using these data together with data from the
literature, we determined improved periods for all variables. For mos
t of the Cepheids, these revised periods lead to excellent, low-noise
light curves, but for a few variables, the periods are obviously varia
ble.