Natural language inference (NLI) data has proven useful in benchmarking and, especially, as pretraining data for tasks requiring language understanding. However, the crowdsourcing protocol that was used to collect this data has known issues and was not explicitly optimized for either of these purposes, so it is likely far from ideal. We propose four alternative protocols, each aimed at improving either the ease with which annotators can produce sound training examples or the quality and diversity of those examples. Using these alternatives and a fifth baseline protocol, we collect and compare five new 8.5k-example training sets. In evaluations focused on transfer learning applications, our results are solidly negative, with models trained on our baseline dataset yielding good transfer performance to downstream tasks, but none of our four new methods (nor the recent ANLI) showing any improvements over that baseline. In a small silver lining, we observe that all four new protocols, especially those where annotators edit pre-filled text boxes, reduce previously observed issues with annotation artifacts.