The problem of stance detection from Twitter tweets, has recently gained significant research attention. This paper addresses the problem of detecting the stance of given tweets, with respect to given topics, from user-generated text (tweets). We use the SemEval 2016 stance detection task dataset. The labels comprise of positive, negative and neutral stances, with respect to given topics. We develop a two-phase feature-driven model. First, the tweets are classified as neutral vs. non-neutral. Next, non-neutral tweets are classified as positive vs. negative. The first phase of our work draws inspiration from the subjectivity classification and the second phase from the sentiment classification literature. We propose the use of two novel features, which along with our streamlined approach, plays a key role deriving the strong results that we obtain. We use traditional support vector machine (SVM) based machine learning. Our system (F-score: 74.44 for SemEval 2016 Task A and 61.57 for Task B) significantly outperforms the state of the art (F-score: 68.98 for Task A and 56.28 for Task B). While the performance of the system on Task A shows the effectiveness of our model for targets on which the model was trained upon, the performance of the system on Task B shows the generalization that our model achieves. The stance detection problem in Twitter is applicable for user opinion mining related applications and other social influence and information flow modeling applications, in real life.