In this paper we propose a novel data hiding procedure called Quantized Projection (QP), that combines elements from quantization (i.e. Quantization Index Modulation, QIM) and spread-spectrum methods. The method is based in quantizing a diversity projection of the host signal, inspired in the statistic used for detection in spread-spectrum algorithms. We carry on a theoretical analysis of QP together with its empirical validation to rigorously show that it offers an excellent performance: QP features probabilities of decoding error several orders of magnitude lower than the aforementioned families of methods for the same dimensionality (diversity) and attacking distortion level. In addition we introduce a Costa-based improvement of the basic QP method named Distortion Compensated QP.