Tolerance and persistence are states that allow non-genetically resistant bacterial cells to survive periods of bactericidal concentrations. Compared to resistance, tolerance and persistence appear to be more diverse in their mechanisms but are less studied. Here we report, using a high throughput microfluidic single-cell microfluidic device, selection for and phenomenological characteristics of cells exposed to recurring exposure to antibiotics. We find a high fraction of tolerant cells, these cells reduce their growth rate but do not go into slow growth or growth arrest, a characteristic previously reported on. Here, tolerance is induced by antibiotic exposure and not caused by a stochastic switch or predetermined state. The tolerance state only weakly depends on the applied concentration of the antibiotic and post-antibiotic exposure there is no fast resumption of growth contrasting again with previous studies. Tolerant cells remain susceptible to antibiotic exposure suggesting recurrent selection for tolerance. Selection also did not act primarily on cells showing relatively high growth rates, as often assumed under exposure to a β-lactam antibiotic. The cells with relatively high growth rates, but still reduced growth compared to prior antibiotic exposure conditions, showed equal mortality risk than cells that were in growth arrest or shrank, slowly growing cells showed the lowest mortality risk. Relatively fast-growing cells and non-growing or shrinking cells exhibited less robust growth patterns compared to slowly, but constantly, growing cells. Our findings suggest a type of tolerance that differs from previously described tolerance and persister characteristics. The high frequency of such tolerant cells, in combination with the fact that they do not arise from growth arrested cells and do not go into growth arrest under antibiotic exposure, suggest that they might play an important role for the evolution to resistance and for antibiotic treatment failure of recurring infections.