Perhaps you could tell us what you might mean by dishonest?

There are quite a number of pretty recent good histories of the War, like Don Higginbotham's The War of American Independence (He's written other books on the war that are highly regarded, I just haven't read them). If you are looking for a political account, the ideas, Gordon Wood's writings, like The Creation of the American Republic , are excellent. He's really mastered his source material.

If by "account" you mean, first person narratives, honesty is not the same as unbiased and omniscient, which is why you'd want to start with a good secondary source first. But there are a few good ones. Thomas Jones wrote an account , History of New York During the Revolutionary War, that was highly critical of it- he was a Loyalist judge, and had to flee. He thought the Revolution was a bad thing. Joseph Plumb Martin wrote an account of being a soldier in the Continental Army, so he thought the reverse- he fought on the other side. Both men could be considered honest, and both men recounted things extremely valuable to historians: Jones for example tells about the colonials' recapture of the slaves, after the surrender at Yorktown, who had previously escaped and taken refuge with the British. Martin, writing decades after the War, was still recalling the several times someone had fed him well as a soldier- recalling exactly what he was given to eat. While he was also perhaps working from a journal kept from the time, it is highly indicative of how well the Army was feeding its troops.

Jones' book is over on Google Books

Martin's book was in print for quite some time as Private Yankee Doodle