Compound verbs aren't always bad, but they can lead to wordy and limp writing. Here's a particularly egregious example:
If he had cheated on his exam, he wouldn't have been able to graduate from college when he had wanted to.
This sentence does three things wrong. First, half of the words are unnecessary. Second, readers will stumble over each compound verb form. Third, the "if/then" nature of the sentence makes it unclear what is actually happening.
To fix this sentence, replace each compound verb with a one-word verb:
If he had cheated changes to He cheated
he wouldn't have been able to changes to he couldn't
he had wanted to changes to he wanted
The final change I'd recommend is to change the entire sentence from a hypothetical event to an actual event, which will eliminate the distracting "if/then" structure. Remember, hypothetical things don't really happen, and your readers will stumble when you force them to consider, simultaneously, two possible versions of reality.
Instead, just give them one version in the simple past tense. It will be simpler, clearer and far more forceful:
He cheated. And couldn't graduate from college.
Yes, the original sentence had more nuance and a different meaning. It's more qualified. But qualified writing bores and has no backbone. Writing should never be hypothetical.