Context: Being able to select the essential, nonnegotiable product features is a key skill for stakeholders of software projects. Such selection relies on human judgment, sometimes supported by structured prioritization techniques and associated tools. Goal: Our goal was to investigate whether certain attributes of prioritization techniques affect stakeholders' threshold for judging product features as essential. The four investigated techniques reflect four combinations of granularity (low, high) and cognitive support (low, high). Method: In one experiment, 94 subjects in four treatment groups indicated the features (from a list of 16) that would be essential in their decision to buy a new cell phone. With a similar setup in a controlled field experiment, 44 domain experts indicated the software product features that were essential for the fulfillment of the project's vision. The effects of granularity and cognitive support on the number of essential ratings were analyzed and compared between the experiments. Result: With lower granularity, significantly more features were rated as essential. The effect was large in the first experiment and extreme (Cohen's d=2.40) in the second. Added cognitive support had medium effect (Cohen's d=0.43 and 0.50), but worked in opposite directions in the two experiments, and was not statistically significant in the second. Implications: The results of the study imply that software projects should avoid taking stakeholders' judgments of essentiality at face value. Practices and tools should be designed to counteract potentially harmful biases; however, more empirical work is needed to obtain more insight into the causes of these biases.