We present a theoretical study of K-shell photodetachment of C − 2 and C − 3 ions. The calculations were carried out using the complex Kohn variational method. Our study addresses the recent observation that what appears as a single, narrow shape resonance close to threshold in the K-shell photodetachment of C − splits into several peaks in the longer C − n carbon anion chains, with the number of peaks increasing with increasing n-values. We argue that the number of expected peaks is related to the number of symmetry-equivalent carbon atoms.