Imagine a world where Google parent Alphabet, at $2tn the world’s fourth-largest listed company, is torn asunder. Its search engine goes one way, the Android operating system another. Web browser Chrome, advertising businesses, all set free in the name of fostering competition. It’s a world Google’s detractors might welcome, but not the one investors see.

The US Department of Justice on Tuesday set out potential ways to defang Google’s illegal monopoly in general internet search. Its ideas, which a judge will consider over the coming year, range from the relatively mild, such as limiting payments to smartphone makers in return for exclusivity on their devices, to so-called structural remedies — in other words, a break-up. A day earlier, another judge decreed Google must open up the Play Store, its shopfront for apps, to competition.

The cases — plus a third one over advertising technology — are complex, but boil down to a common idea: Google has created innovative products users and advertisers love, but then used overly sharp-elbowed tactics to entrench them. Curtailing those specific practices, be they the near-$20bn it pays iPhone-maker Apple to displace other search engines on its devices, or the up-to-30 per cent rents imposed on in-app payments, sounds sensible.