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Large-scale natural language inference (NLI) datasets such as SNLI or MNLI have been created by asking crowdworkers to read a premise and write three new hypotheses, one for each possible semantic relationships (entailment, contradiction, and neutral). While this protocol has been used to create useful benchmark data, it remains unclear whether the writing-based annotation protocol is optimal for any purpose, since it has not been evaluated directly. Furthermore, there is ample evidence that crowdworker writing can introduce artifacts in the data. We investigate two alternative protocols which automatically create candidate (premise, hypothesis) pairs for annotators to label. Using these protocols and a writing-based baseline, we collect several new English NLI datasets of over 3k examples each, each using a fixed amount of annotator time, but a varying number of examples to fit that time budget. Our experiments on NLI and transfer learning show negative results: None of the alternative protocols outperforms the baseline in evaluations of generalization within NLI or on transfer to outside target tasks. We conclude that crowdworker writing still the best known option for entailment data, highlighting the need for further data collection work to focus on improving writing-based annotation processes.