There has been some debate as to the meaning of this song. "Some rival" (corrupted at times into "some rifle") is simple enough, but "some tyrant" often seems to trigger imaginative speculation on the involvement of some monarch or other. There doesn't seem to be any internal evidence to support this, but "the Americans" and "the merry king" both occur instead in the first lines of some versions, which tends to confuse the issue. The one is presumably a corruption of the other, but it is difficult to say which would be the earlier form.

Lucy Broadwood's reference in Traditional English Songs and Carols (1908 p. 125) to a ballad printed in the first half of the 17th century, A courtly new ballad of the princely wooing of the fair maid of London by king Edward, further confuses the matter: Miss Broadwood wondered whether Edward IV might be the "merry king", and people have since not infrequently taken her remark to indicate a firm connection with Some Rival (Lesley Nelson goes a step further and states without evidence that it is another version of it, though that isn't what Miss Broadwood said) but the only clear connection is the fact that, in common with a number of other otherwise unrelated songs, they were set to the same tune. Fair Angel of England, the tune indicated for Price's Loves fierce desire, derived its name from the first line of the "courtly new ballad": this was set to Bonny sweet Robin, which so far as we can tell was the original name of the tune. (See Simpson, The British Broadside Ballad and Its Music, 1966, 59-64.)

The full text of Price's Loves fierce desire is transcribed at Bruce Olson's site:

Loves fierce desire, and hopes of Recovery