The winner-minus-loser (WML) momentum strategy carries an inherent downside as its returns have negative coskewness. We propose a coskewness-volatility-managed momentum strategy that reduces the reversal risk of the baseline WML strategy by 61% and that of the volatility-managed momentum strategy (Barosso and Santa-Clara, 2015) by 20% for US stocks. The returns of our strategy generate a slightly positive skewness in contrast with the negative skewness of the WML and volatility-managed strategies. Since the coskewness of momentum portfolio returns predict future returns for up to 12 months, our strategy is effective for momentum portfolios of holding periods longer than one month. Our strategy also mitigates momentum downside risks in major international stock markets such as the UK, Germany, and France.