diff --git a/src/Database.elm b/src/Database.elm
index a1032cb..6ce0634 100644
--- a/src/Database.elm
+++ b/src/Database.elm
@@ -147,7 +147,7 @@ type QueryPlan
     = Read String
     | Select Selection QueryPlan
     | Project (List Field) QueryPlan
-    | Join { left : QueryPlan, leftFields : List Field, right : QueryPlan, rightFields : List Field }
+    | Join { left : QueryPlan, right : QueryPlan, fields : List ( Field, Field ) }
 
 
 runPlan : QueryPlan -> Database -> Result Problem Relation
@@ -197,14 +197,20 @@ runPlan plan ((Database db) as db_) =
                                     Err err ->
                                         Err err
                             )
+
+                leftFields =
+                    List.map Tuple.first config.fields
+
+                rightFields =
+                    List.map Tuple.second config.fields
             in
             Result.map2
                 (\left right ->
-                    if takeFields config.leftFields left.schema /= takeFields config.rightFields right.schema then
+                    if takeFields leftFields left.schema /= takeFields rightFields right.schema then
                         Err
                             (SchemaMismatch
-                                { wanted = takeFields config.leftFields left.schema
-                                , got = takeFields config.rightFields right.schema
+                                { wanted = takeFields leftFields left.schema
+                                , got = takeFields rightFields right.schema
                                 }
                             )
 
@@ -213,7 +219,7 @@ runPlan plan ((Database db) as db_) =
                             leftIndex =
                                 List.foldl
                                     (\row ->
-                                        Sort.Dict.update (takeFields config.leftFields row)
+                                        Sort.Dict.update (takeFields leftFields row)
                                             (\maybeRows ->
                                                 case maybeRows of
                                                     Just rows ->
@@ -231,7 +237,7 @@ runPlan plan ((Database db) as db_) =
                             , rows =
                                 List.concatMap
                                     (\rightRow ->
-                                        case Sort.Dict.get (takeFields config.rightFields rightRow) leftIndex of
+                                        case Sort.Dict.get (takeFields rightFields rightRow) leftIndex of
                                             Just rows ->
                                                 List.map (\leftRow -> Array.append leftRow rightRow) rows
 
@@ -241,8 +247,8 @@ runPlan plan ((Database db) as db_) =
                                     right.rows
                             }
                 )
-                (runInput config.left config.leftFields)
-                (runInput config.right config.rightFields)
+                (runInput config.left leftFields)
+                (runInput config.right rightFields)
                 |> Result.andThen identity
 
 
diff --git a/src/Datalog.elm b/src/Datalog.elm
index a9d51cc..936b3f9 100644
--- a/src/Datalog.elm
+++ b/src/Datalog.elm
@@ -34,8 +34,12 @@ ruleToPlan (Rule (Atom _ headTerms) bodyAtoms) =
                             let
                                 ( leftNames, leftPlan ) =
                                     atomToPlan nextAtom
-
-                                fields =
+                            in
+                            ( leftNames ++ rightNames
+                            , Database.Join
+                                { left = leftPlan
+                                , right = rightPlan
+                                , fields =
                                     Dict.merge
                                         (\_ _ soFar -> soFar)
                                         (\_ left right soFar -> ( left, right ) :: soFar)
@@ -43,13 +47,6 @@ ruleToPlan (Rule (Atom _ headTerms) bodyAtoms) =
                                         (Dict.fromList (List.indexedMap (\i field -> ( field, i )) leftNames))
                                         (Dict.fromList (List.indexedMap (\i field -> ( field, i )) rightNames))
                                         []
-                            in
-                            ( leftNames ++ rightNames
-                            , Database.Join
-                                { left = leftPlan
-                                , leftFields = List.map Tuple.first fields
-                                , right = rightPlan
-                                , rightFields = List.map Tuple.second fields
                                 }
                             )
                         )
diff --git a/tests/DatabaseTests.elm b/tests/DatabaseTests.elm
index 82f6d25..fb28942 100644
--- a/tests/DatabaseTests.elm
+++ b/tests/DatabaseTests.elm
@@ -191,9 +191,8 @@ runPlanTests =
                             (runPlan
                                 (Join
                                     { left = Read "mascots"
-                                    , leftFields = [ 3 ]
                                     , right = Read "teams"
-                                    , rightFields = [ 0 ]
+                                    , fields = [ ( 3, 0 ) ]
                                     }
                                 )
                             )
@@ -205,9 +204,8 @@ runPlanTests =
                             (runPlan
                                 (Join
                                     { left = Read "mascots"
-                                    , leftFields = [ 0 ]
                                     , right = Read "teams"
-                                    , rightFields = [ 4 ]
+                                    , fields = [ ( 0, 4 ) ]
                                     }
                                 )
                             )
@@ -219,9 +217,8 @@ runPlanTests =
                             (runPlan
                                 (Join
                                     { left = Read "mascots"
-                                    , leftFields = [ 0 ]
                                     , right = Read "teams"
-                                    , rightFields = [ 3 ]
+                                    , fields = [ ( 0, 3 ) ]
                                     }
                                 )
                             )
@@ -233,27 +230,6 @@ runPlanTests =
                                     }
                                 )
                             )
-            , test "it's an error if you join on different numbers of keys" <|
-                \_ ->
-                    mascotsDb
-                        |> Result.andThen
-                            (runPlan
-                                (Join
-                                    { left = Read "mascots"
-                                    , leftFields = [ 0, 1 ]
-                                    , right = Read "teams"
-                                    , rightFields = [ 0 ]
-                                    }
-                                )
-                            )
-                        |> Expect.equal
-                            (Err
-                                (SchemaMismatch
-                                    { wanted = Array.fromList [ StringType, StringType ]
-                                    , got = Array.fromList [ StringType ]
-                                    }
-                                )
-                            )
             , test "joins on fields in order" <|
                 \_ ->
                     mascotsDb
@@ -261,9 +237,8 @@ runPlanTests =
                             (runPlan
                                 (Join
                                     { left = Read "mascots"
-                                    , leftFields = [ 1 ]
                                     , right = Read "teams"
-                                    , rightFields = [ 0 ]
+                                    , fields = [ ( 1, 0 ) ]
                                     }
                                 )
                             )
@@ -284,9 +259,8 @@ runPlanTests =
                             (runPlan
                                 (Join
                                     { left = Read "mascots"
-                                    , leftFields = []
                                     , right = Read "teams"
-                                    , rightFields = []
+                                    , fields = []
                                     }
                                 )
                             )
diff --git a/tests/DatalogTests.elm b/tests/DatalogTests.elm
index 73c4b03..569b596 100644
--- a/tests/DatalogTests.elm
+++ b/tests/DatalogTests.elm
@@ -37,9 +37,8 @@ datalogTests =
                         |> Expect.equal
                             (Database.Join
                                 { left = Database.Read "reachable"
-                                , leftFields = [ 0 ]
                                 , right = Database.Read "link"
-                                , rightFields = [ 1 ]
+                                , fields = [ ( 0, 1 ) ]
                                 }
                                 |> Database.Project [ 2, 1 ]
                                 |> Ok