Secondary structure and solvent accessibility prediction provide valuable information for estimating the three dimensional structure of a protein. As new feature extraction methods are developed the dimensionality of the input feature space increases steadily. Reducing the number of dimensions provides several advantages such as faster model training, faster prediction and noise elimination. In this work, several dimensionality reduction techniques have been employed including various feature selection methods, autoencoders and PCA for protein secondary structure and solvent accessibility prediction. The reduced feature set is used to train a support vector machine at the second stage of a hybrid classifier. Cross-validation experiments on two difficult benchmarks demonstrate that the dimension of the input space can be reduced substantially while maintaining the prediction accuracy. This will enable the incorporation of additional informative features derived for predicting the structural properties of proteins without reducing the accuracy due to overfitting.