High Dynamic Range (HDR) reconstruction is the process of producing an HDR image from a set of Standard Dynamic Range (SDR) images with different exposure times. This is a particularly challenging problem when relative camera or object motion exists between the available SDR images. Recently, deep learning methods, specifically those based on convolutional neural networks (CNNs) have been developed for HDR and shown to achieve unprecedented quality gains. Invariably an image alignment phase precedes the CNN mapping and merging. In practice, this alignment step greatly increases the computational burden of deep HDR methods often rendering them unsuitable for real-time composition. We propose a new deep HDR technique that does not need any explicit alignment of SDR images. Instead, a novel attention mask is developed that enables the network to focus on parts of the scene with considerable motion. Further, a dense merger is proposed that leads to an economical network. Evaluation over benchmark databases reveals that the proposed AttenDense network achieves high quality HDR results with significantly reduced computation time than state of the art. Further, the incorporation of domain knowledge (development of a custom attention mask) allows a more graceful decay in performance in the face of limited training.