The present study concerns depth-k pooling for building IR test collections. At TREC, pooled documents are traditionally presented in random order to the assessors to avoid judgement bias. In contrast, an approach that has been used widely at NTCIR is to prioritise the pooled documents based on “pseudorelevance,” in the hope of letting assessors quickly form an idea as to what constitutes a relevant document and thereby judge more efficiently and reliably. While the recent TREC 2017 Common Core Track went beyond depth-k pooling and adopted a method for selecting documents to judge dynamically, even this task let the assessors process the usual depth-10 pools first: the idea was to give the assessors a “burn-in” period, which actually appears to echo the view of the NTCIR approach. Our research questions are: (1) Which depth-k ordering strategy enables more efficient assessments? Randomisation, or prioritisation by pseudorelevance? (2) Similarly, which of the two strategies enables higher inter-assessor agreements? Our experiments based on two English web search test collections with multiple sets of graded relevance assessments suggest that randomisation outperforms prioritisation in both respects on average, although the results are statistically inconclusive. We then discuss a plan for a much larger experiment with sufficient statistical power to obtain the final verdict.