ST_CoveredBy — Returns true if no point in A is outside B
boolean ST_CoveredBy(geometry 
      geomA, geometry 
      geomB);
boolean ST_CoveredBy(geography 
      geogA, geography 
      geogB);
Returns true if no point in Geometry/Geography A lies outside
            Geometry/Geography B.
            Equivalently, tests if every point of geometry A is inside
            (i.e. intersects the interior or boundary of) geometry B.
            
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This function automatically includes a bounding box comparison
that makes use of any spatial indexes that are available on the geometries.
         To avoid index use, use the function   | 
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Enhanced: 3.0.0 enabled support for   | 
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Do not use this function with invalid geometries. You will get unexpected results.  | 
Performed by the GEOS module
Availability: 1.2.2
NOTE: this is the "allowable" version that returns a boolean, not an integer.
Not an OGC standard, but Oracle has it too.
  --a circle coveredby a circle
SELECT ST_CoveredBy(smallc,smallc) As smallinsmall,
  ST_CoveredBy(smallc, bigc) As smallcoveredbybig,
  ST_CoveredBy(ST_ExteriorRing(bigc), bigc) As exteriorcoveredbybig,
  ST_Within(ST_ExteriorRing(bigc),bigc) As exeriorwithinbig
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
  ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
  --Result
 smallinsmall | smallcoveredbybig | exteriorcoveredbybig | exeriorwithinbig
--------------+-------------------+----------------------+------------------
 t            | t                 | t                    | f
(1 row)