Stopping randomized trials early because of an apparent benefit is becoming more common. To protect and promote the interests of trial participants, investigators may feel obligated to stop a trial early because of the apparent benefit of a study treatment (compared with placebo or other treatment). There are, however, serious ethical problems with doing so. Truncated trials systematically overestimate treatment effects; in cases where the number of accrued outcome events is small, the overestimation may be very large. Generating seriously inflated estimates of treatment effect violates the ethical research requirement of scientific validity. Subsequent use of inflated estimates to inform clinical decision making and practice guidelines violates the ethical requirements of social value and a favorable risk-benefit ratio. Researchers should ensure that a large number of outcome events accrues before stopping a trial and then continue recruitment to assess whether positive trends continue. This can balance the need to protect research participants with the ethical requirements of scientific validity, social value, and a favorable risk-benefit ratio.