The five lowest J rotational transitions of (13)C(16)O have been measured by saturation-dip spectroscopy to an accuracy of about 2 kHz, employing phase-stabilized backward-wave oscillators (BWOs). These highly precise measurements cover the transitions from J = 2 <-- 1 to J = 6 <-- 5 with frequencies ranging from 220 to 661 GHz. For each of the five observed rotational transitions, the narrow linewidths of the saturation dips (about 20 kHz) permitted the resolution of the hyperfine splitting for the first time. This splitting is caused by the (13)C-nuclear spin-rotation interaction yielding a value for the nuclear spin-rotation coupling constant of C(I)((13)C(16)O). If combined with the beam measurements (C(I)((13)C(16)O) = 32.63(10) kHz), a slight J-dependence of the spin-rotation coupling constant can be determined (C(J) = 30 +/- 13 Hz). In addition, we have measured in the Doppler-limited mode several higher J rotational line positions of (13)C(16)O up to 991 GHz with an accuracy of 5 kHz. The two line positions (J = 12 <-- 11 and J = 14 <-- 13) were recorded by multiplying BWO frequency with an accuracy of 100 kHz. The rotational transitions J = 17 <-- 16 and J = 18 <-- 17 were measured with an accuracy between 15 and 25 kHz by using the Cologne sideband spectrometer for terahertz applications COSSTA. Copyright 2000 Academic Press.