How to make `paste` command stop on shortest file

I have two files: **a.txt** 1 2 3 **b.txt** foo bar baz qux Running paste a.txt b.txt gives 1 foo 2 bar 3 baz qux However I want to stop when the shortest file ends (that is, I want to print only complete rows, otherwise a later program down the pipeline will think qux is the first field and the second is empty, when really it's the only way around). How can I do this?