Does a multi-engine ATP with single-engine commercial privileges provide single-engine instrument privileges? Does a multi-engine ATP with single-engine commercial privileges provide single-engine instrument privileges?

I received my ATP certificate recently, and the back of my FAA certificate reads as follows.

AIRLINE TRANSPORT PILOT
  AIRPLANE MULTIENGINE LAND
  ...
COMMERCIAL PRIVILEGES
  AIRPLANE SINGLE ENGINE LAND
...


I left out the specific type ratings and limitations as noted by ....

The ATP supersedes an instrument rating, but the ATP is for the multi-engine category. Shouldn't the certificate reflect an instrument rating in the single-engine category?

The changes to my certificate were completed in IACRA and I have had part of a rating inadvertently removed before using the IACRA system.
Note this is my interpretation of part 61. Double check with the FSDO for a more legally biding answer.

Since the Instrument addon is by category, not class, aka Instrument Airplane, or Instrument Rotorcraft, the ATP Multi-Engine Airplane, counts for Instrument Airplane for the Commercial Single.