Lowest API calls to retrieve contacts related to multiple accounts?

Lowest API calls to retrieve contacts related to multiple accounts?

To get all the Accounts  associated  with Contacts can searchRecords or getRecords for Contacts then   getRecordById with &idlist to get Account records.

Not seeing a good way to do the reverse because ContactsId is not stored in the Accounts record.
Could do searchRecords or getRecords on Accounts and getRecords or  getRelated for Contacts but getRelated maybe greater number of calls compared to getRecords.
Is there a way for less API calls for Contacts?

Regards,
Glenn