The redundancy here is less evident. For a dramatic sense of the difference revision makes, you might try computing the Lard Factor in a few of your sentences. After revising a sentence, subtract the number of words in the revised version from the number of words in the original. Then divide the remainder by the number in the original. It's not necessary to say what's obviously implied.
Good writers use adjectives and adverbs sparingly.
As Strunk's advice suggests, the problem is not one of absolute numbers. It's not many words but unnecessary words that obscure meaning and make prose leaden. Lively writing has other enemies than wordiness. Avoid excessive use of the verb to be. Use the passive voice sparingly.