Antibiotic-resistant bacteria are a significant threat to human health, with one estimate suggesting they will cause 10 million worldwide deaths per year by 2050, surpassing deaths due to cancer1. Because new antibiotic development can take a decade or longer, it is imperative to effectively use currently available drugs. Antibiotic combination therapy offers promise for treating highly resistant bacterial infections, but the factors governing the sporadic efficacy of such regimens have remained unclear. Dogma suggests that antibiotics ineffective as monotherapy can be effective in combination2. Here, using carbapenem-resistant Enterobacteriaceae (CRE) clinical isolates, we reveal the underlying basis for the majority of effective combinations to be heteroresistance. Heteroresistance is a poorly understood mechanism of resistance reported for different classes of antibiotics3-6 in which only a subset of cells are phenotypically resistant7. Within an isolate, the subpopulations resistant to different antibiotics were distinct, and over 88% of CRE isolates exhibited heteroresistance to multiple antibiotics ('multiple heteroresistance'). Combinations targeting multiple heteroresistance were efficacious, whereas those targeting homogenous resistance were ineffective. Two pan-resistant Klebsiella isolates were eradicated by combinations targeting multiple heteroresistance, highlighting a rational strategy to identify effective combinations that employs existing antibiotics and could be clinically implemented immediately.