Advanced Search - Limit Specify Criteria

Advanced Search - Limit Specify Criteria

Is there anyone who can advise on whether you can disable certain fields from appearing in the 'Specify Criteria' option within Advanced Search. 

It seems by Default that every single field you create in a module appears in the dropdown which are also not in alphabetical order. This just looks incredibly messy and we would only use half of these fields to run a search anyway. Is there a way where we can make fields not appear in the Advanced Search / Specify Criteria drop down or at least sort them by alphabetical order?