[amelia] Imputation model: a trade off?

Dear all I have a question concerning the inclusion of (auxiliary) variables into the missing data procedure. I understand that a rather "inclusive" strategy can increase efficiency and reduced bias. Now, I also have the feeling that the inclusion of a certain (auxiliary) variable can have an additional cost that depends on the degree of missingness of this (auxiliary) variable itself. If the latter is "too high", couldn't this result in a higher disadvantage of including this variable relative to the advantage (increase in efficiency and/or reduced bias) that the inclusion of the variable could have? If yes, does there exist a measure/rule of thumb to evaluate and judge on this trade off? Thank you for your efforts. Philippe