The early error detection capabilities of syntax-driven parsers are studied. The classes of weak precedence and simple mixed-strategy precedence parsers are chosen as the object of study. Very similar techniques could be used to obtain related results for other classes of syntax-driven parsers. We investigate whether the correct-prefix and the viable-prefix properties can be enforced within these classes: A negative result is obtained for the first class and a positive one for the second. Moreover, for the simple mixed-strategy class the relationship between early error detection and parser size is studied. Some lower bounds on the parser size are proven for simple mixed-strategy precedence parsers that have the viable-prefix property.