Statistical spam filters are known to be vulnerable to ad- versarial attacks. One such adversarial attack, known as the Good Word Attack, thwarts spam filters by appending to spam messages sets of "good" words, which are common in legitimate e-mail but rare in spam. We present a counter- attack strategy that first attempts to differentiate spam from legitimate e-mail in the input space, by transforming each e- mail into a bag of multiple segments, and subsequently ap- plies multiple instance logistic regression on the bags. We treat each segment in the bag as an instance. An e-mail is classified as spam if at least one instance in the corre- sponding bag is spam, and as legitimate if all the instances in it are legitimate. We show that a spam filter using our multiple instance counter-attack strategy stands up better to good word attacks than its single instance counterpart and the commonly practiced Bayesian filters.