No. 1 with a T-shirt?

For decades, the phrase “No. 1 with a bullet” has referred to a song or album that zooms to the top of the Billboard charts. Given current music industry practices, “No. 1 with a T-shirt” may be more accurate.

Lately, many artists — and their record companies — have been trying to game the system of ranking musical hits by including free downloads of new albums with sales of concert tickets, clothing and other merchandise. It’s a widespread practice, and the result is some confusion about what, exactly, the weekly charts are measuring.

Now some of the very people who have taken advantage of this strategy are complaining about it, and Billboard is under pressure to change the rules governing its charts.

The use of album bundles — tacking a download or CD to another purchase — is an age-old sales gimmick in the music industry, but now it’s everywhere. Of the 39 titles that went to No. 1 last year, at least 18 were sold as part of ticket or merchandise deals. One of the most prolific bundlers has been Houston rapper Travis Scott, who last year claimed the top spot by selling key chains, hats and access to concert tickets.

The next big bundler may be Taylor Swift. While her new album has no announced release date, her website is already accepting advance orders for it as part of deals for a hoodie ($65), a T-shirt ($40) and a smartphone stand (a bargain at $20), in hopes of its hitting No. 1 once it comes out.

At the same time, behind-the-scenes disputes have broken out between artists and Billboard’s chart referees when the trade publication deems particular deals out of bounds, potentially costing musicians their shot at the top slot.

Last month, there were two such disagreements: first when a Christian rock group, Hillsong United, lost out for No. 1 to Pink after some of its ticket deals were...