The cWINNOWER algorithm detects fuzzy motifs in DNA sequences rich in proteinbinding signals. A signal is defined as any short nucleotide pattern having up to d mutations differing from a motif of length l. The algorithm finds such motifs if a clique consisting of a suffciently large number of mutated copies of the motif (i.e., the signals) is present in the DNA sequence. The cWINNOWER algorithm substantially improves the sensitivity of the winnower method of Pevzner and Sze by imposing a consensus constraint, enabling it to detect much weaker signals. We studied the minimum detectable clique size q_c as a function of sequence length N for random sequences. We found that q_c increases linearly with N for a fast version of the algorithm based on counting threemember sub-cliques. Imposing consensus constraints reduces q_c by a factor of three in this case, which makes the algorithm dramatically more sensitive. Our most sensitive algorithm, which counts four-member sub-cliques, needs a minimum of only 13 signals to detect motifs in a sequence of length N=12,000 for (l,d)=(15,4).