Skin cancer is one of the major types of cancers with an increasing incidence over the past decades. Accurately diagnosing skin lesions to discriminate between benign and malignant skin lesions is crucial to ensure appropriate patient treatment. While there are many computerised methods for skin lesion classification, convolutional neural networks (CNNs) have been shown to be superior over classical methods. In this work, we propose a fully automatic computerised method for skin lesion classification which employs optimised deep features from a number of well-established CNNs and from different abstraction levels. We use three pre-trained deep models, namely AlexNet, VGG16 and ResNet-18, as deep feature generators. The extracted features then are used to train support vector machine classifiers. In the final stage, the classifier outputs are fused to obtain a classification. Evaluated on the 150 validation images from the ISIC 2017 classification challenge, the proposed method is shown to achieve very good classification performance, yielding an area under receiver operating characteristic curve of 83.83% for melanoma classification and of 97.55% for seborrheic keratosis classification.