The cavity ring-down laser method using a continuously tunable titanium:sapphire ring laser with an external high-finesse cavity has been used to record a high-resolution overtone spectrum of a gaseous (C2H2)-C-12 sample in the wavenumber region 12260-12380 cm(-1). A direct non-linear least-squares fitting of the ring-down signal is found to lead to increased sensitivity when compared with the linear least-squares methods. Two new bands have been observed and rotationally analysed. A comparison of the new results with previous theoretical work shows a good agreement.