Machine comprehension is a representative task of natural language understanding. Typically, we are given context paragraph and the objective is to answer a question that depends on the context. Such a problem requires to model the complex interactions between the context paragraph and the question. Lately, attention mechanisms have been found to be quite successful at these tasks and in particular, attention mechanisms with attention flow from both context-to-question and question-to-context have been proven to be quite useful. In this paper, we study two state-of-the-art attention mechanisms called Bi-Directional Attention Flow (BiDAF) and Dynamic Co-Attention Network (DCN) and propose a hybrid scheme combining these two architectures that gives better overall performance. Moreover, we also suggest a new simpler attention mechanism that we call Double Cross Attention (DCA) that provides better results compared to both BiDAF and Co-Attention mechanisms while providing similar performance as the hybrid scheme. The objective of our paper is to focus particularly on the attention layer and to suggest improvements on that. Our experimental evaluations show that both our proposed models achieve superior results on the Stanford Question Answering Dataset (SQuAD) compared to BiDAF and DCN attention mechanisms.