The existing literature in insurance economics has shown that narrow framing can explain why people buy too little insurance compared to what standard theory predicts. However, there is also ample evidence suggesting people sometimes buy too much insurance. In this paper, we assume S-shaped narrow framing, i.e., the local utility function for evaluating the net insurance payoff is convex in the loss domain but concave in the gain domain, and show that it can reconcile with both insurance puzzles simultaneously. Especially, we show the policyholder under S-shaped narrow framing is more likely to underinsure more negatively skewed risks of loss but to overinsure less negatively skewed risks of loss when only coinsurance is offered. We further characterize the optimal insurance scheme under S-shaped narrow framing while incentive compatibility is satisfied. It contains a straight deductible when the net insurance payoff is negative but partial insurance when the net insurance payoff is positive.