Parental use of private literacy tutoring has been one of the most controversial of the 'unintended outcomes' of the introduction of the National Assessment Program--Literacy and Numeracy (NAPLAN), Australia's national regimen of literacy testing. Other uses of tutoring--whether NAPLAN-related or not--have attracted less public and research attention. This article reports an exploratory interview study of the implication of NAPLAN in parents' use of tutoring with children who were in Year 5 in 2017. It describes two categories of NAPLAN-related tutoring (NAPLAN coaching and NAPLAN-responsive tutoring) and a category of tutoring to which NAPLAN was at best incidental. The study theorised NAPLAN as a technology that responsibilises parents for their children's educational success and life chances. Drawing on concepts from Pierre Bourdieu's sociology, it theorised parental action on the tutoring market as strategic practice. A relational analytic method was used which looked at the co-occurrence of the three categories of tutoring with categories of performance/ability; risks to achievement and problems in learning; and income and other parental resources. Findings show that NAPLAN-related tutoring was an object of strategies that played out differently according to parents' perceptions and classifications of their children's individual ability/performance, the role NAPLAN had served in alerting parents to literacy problems or in certifying a child's high performance, and the resources the family could deploy as they acted on behalf of their child. Implications for understanding NAPLAN-related tutoring as more probable in some families than in others are drawn, along with a suggestion for further research to quantify the findings of this exploratory study.