Coming late to the party, but since I had the additional requirement of having one word per line, this one addition did the trick for me:
label.numberOfLines = [labelString componentsSeparatedByString:@" "].count;
Apple Docs say:
Normally, the label text is drawn with the font you specify in the font property. If this property is set to YES, however, and the text in the text property exceeds the label’s bounding rectangle, the receiver starts reducing the font size until the string fits or the minimum font size is reached. In iOS 6 and earlier, this property is effective only when the numberOfLines property is set to 1.
But this is a lie. A lie I tell you! It's true for all iOS versions. Specifically, this is true when using a UILabel within a UICollectionViewCell for which the size is determined by constraints adjusted dynamically at runtime via custom layout (ex. self.menuCollectionViewLayout.itemSize = size).
So when used in conjunction with adjustsFontSizeToFitWidth and minimumScaleFactor, as mentioned in previous answers, programmatically setting numberOfLines based on word count solved the autoshrink problem. Doing something similar based on word count or even character count might produce a "close enough" solution.