One of the great things about writing formal poetry is that, if you approach it the right way, it can force you to reduce unnecessary words to meet the structural requirements, and simultaneously add more ideas to meet the rhyme scheme. Here is an example:

Jam Jar

In the night’s jam jar of my memory
My long-dead parents live as fireflies.
My thoughts of them worn by time’s emery,
Their faint light still suggests where my path lies.

(This from the Amsterdam Quarterly, which produces three themed issues a year, the current one being related to “Genealogy”.) The original expression of the image behind the first two lines was longer than the end result; tightening it up and finding “emery” as a rhyme for “memory” extended it again, but this time as a regular quatrain.

If you write an outline of a poem that comes out to 15-20 lines, in free verse but with a couple of rhymes showing up, consider condensing it into a sonnet. All the unnecessary words get squeezed out, and the search for additional rhymes will only make the thoughts richer.

Structure and rhyme can be used to compress, condense, and hopefully intensify the ideas and their expression. But, amusingly, it is also possible to search for rhyme by increasing words, rambling until the rhyme can be tracked down. Scotland’s 19th century William McGonagall comes to mind, his most famous work being “The Tay Bridge Disaster”.

The Tay Bridge Disaster

It tells of the collapse of the railway bridge during a storm, while a passenger train was on it:

Beautiful Railway Bridge of the Silv’ry Tay!
Alas! I am very sorry to say
That ninety lives have been taken away
On the last Sabbath day of 1879,
Which will be remember’d for a very long time.
(…)
I must now conclude my lay
By telling the world fearlessly without the least dismay
That your central girders would not have given way,
At least many sensible men do say,
Had they been supported on each side with buttresses,
At least many sensible men confesses,
For the stronger we our houses do build,
The less chance we have of being killed.

The structural requirements of formal verse are only justified when they are at the service of the poem’s aesthetics (or esthetics, depending on your residence). Rhyme, metre/meter and so on should be thought-provoking or relaxing sources of enjoyment, beauty, humo(u)r, memorableness. There is no merit in rhyme that destroys those things.