diff --git a/src/BooleanObservationTable.hs b/src/BooleanObservationTable.hs
index 378f5bd..c9b306f 100644
--- a/src/BooleanObservationTable.hs
+++ b/src/BooleanObservationTable.hs
@@ -20,16 +20,16 @@ mqToSubset mq = mapFilter (\(i, o) -> maybeIf (fromBool o) i) . mq
 
 -- A table is nothing more than a part of the language.
 -- Invariant: content is always a subset of
--- `rows * columns` union `rows * alph * columns`.
+-- `domain` = `rows * columns` union `rows * alph * columns`.
 data Table i = Table
     { content    :: Set [i]
+    , domain     :: Set [i]
     , rowIndices :: Set (RowIndex i)
     , colIndices :: Set (ColumnIndex i)
     , aa         :: Set i
     }
     deriving (Show, Ord, Eq, Generic, NominalType, Conditional, Contextual)
 
--- Currently, it may ask redundant membership queries
 instance (NominalType i, Contextual i) => ObservationTable (Table i) i Bool where
     type Row (Table i) = Set [i]
     rows = rowIndices
@@ -41,26 +41,31 @@ instance (NominalType i, Contextual i) => ObservationTable (Table i) i Bool wher
 
     addRows mq newRows t@Table{..} =
         t { content = content `union` newContent
+          , domain = domain `union` newPartRed
           , rowIndices = rowIndices `union` newRows
           }
         where
             newRowsExt = pairsWith (\r a -> r ++ [a]) newRows aa
             newPart = pairsWith (++) (newRows `union` newRowsExt) colIndices
-            newContent = mqToSubset mq newPart
+            newPartRed = newPart \\ domain
+            newContent = mqToSubset mq newPartRed
 
     addColumns mq newColumns t@Table{..} =
         t { content = content `union` newContent
+          , domain = domain `union` newPartRed
           , colIndices = colIndices `union` newColumns
           }
         where
             newColumnsExt = pairsWith (:) aa newColumns
             newPart = pairsWith (++) rowIndices (newColumns `union` newColumnsExt)
-            newContent = mqToSubset mq newPart
+            newPartRed = newPart \\ domain
+            newContent = mqToSubset mq newPartRed
 
 
 initialBTableWith :: NominalType i => MQ i Bool -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> Table i
 initialBTableWith mq alphabet newRows newColumns = Table
     { content = content
+    , domain = domain
     , rowIndices = newRows
     , colIndices = newColumns
     , aa = alphabet
diff --git a/src/SimpleObservationTable.hs b/src/SimpleObservationTable.hs
index 4ad4854..384e3b0 100644
--- a/src/SimpleObservationTable.hs
+++ b/src/SimpleObservationTable.hs
@@ -67,9 +67,8 @@ instance (NominalType i, NominalType o) => ObservationTable (Table i o) i o wher
             newContent = mq newPartRed
 
 
--- I could make a more specific implementation for booleans.
--- But for now we reuse the above, and do minor optimisations
-
+-- We can reuse the above tables for the Boolean case and
+-- perform some minor optimisations.
 newtype Boolean table = B { unB :: table }
     deriving (Show, Ord, Eq, Generic, NominalType, Conditional, Contextual)
 
@@ -78,28 +77,22 @@ type BTable i = Boolean (Table i Bool)
 instance (NominalType i) => ObservationTable (BTable i) i Bool where
     -- Special case of a boolean: functions to Booleans are subsets
     type Row (BTable i) = Set [i]
+
+    -- All the reusable functions are simply coerced
     rows = coerce (rows :: _ => Table i Bool -> _)
     cols = coerce (cols :: _ => Table i Bool -> _)
     rowsExt = coerce (rowsExt :: _ => Table i Bool -> _)
     colsExt = coerce (colsExt :: _ => Table i Bool -> _)
     alph = coerce (alph :: _ => Table i Bool -> _)
     tableAt = coerce (tableAt :: _ => Table i Bool -> _)
-    --rows = rowIndices . unB
-    --cols = colIndices . unB
-    --alph = aa . unB
-    --tableAt = tableAt . unB
+    addRows = coerce (addRows :: _ => _ -> _ -> Table i Bool -> Table i Bool)
+    addColumns = coerce (addColumns :: _ => _ -> _ -> Table i Bool -> Table i Bool)
 
-    -- TODO: slightly inefficient
+    -- These are specific to our representation of Row
     row (B Table{..}) r = let lang = mapFilter (\(i, o) -> maybeIf (fromBool o) i) content
                           in filter (\a -> lang `contains` (r ++ a)) colIndices
     rowEps (B Table{..}) = mapFilter (\(i, o) -> maybeIf (fromBool o /\ i `member` colIndices) i) content
 
-    --addRows mq newRows = B . addRows mq newRows . unB
-    addRows = coerce (addRows :: _ => _ -> _ -> Table i Bool -> Table i Bool)
-    --addColumns mq newColumns = B . addColumns mq newColumns . unB
-    addColumns = coerce (addColumns :: _ => _ -> _ -> Table i Bool -> Table i Bool)
-
-type BRow i = Row (BTable i)
 
 initialTableWith :: (NominalType i, NominalType o) => MQ i o -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> Table i o
 initialTableWith mq alphabet newRows newColumns = Table