Should you remove an item from a scale if Cronbach's alpha is already >.90?

In order to determine whether an item should be removed from a scale, I'm aware that I need to look at least 3 types of evidence: the interitem correlation matrix, corrected item-total correlation coefficients, and changes to the cronbach's alpha if the item is deleted. My questions is with regards to the last criteria. If my cronbach's alpha is .91, is it logical to delete items that will increase this value (say to .92 or .93)? I ask because some statisticians suggest that cronbach's alpha should be a maximum of .90 and higher values indicate redundancy (e.g., Streiner, 2003). Thanks in advance for the help!