diff --git a/build/vega-lite-schema.json b/build/vega-lite-schema.json
index 0e99779025..c169ce5c8f 100644
--- a/build/vega-lite-schema.json
+++ b/build/vega-lite-schema.json
@@ -7665,14 +7665,7 @@
         "params": {
           "description": "Dynamic variables or selections that parameterize a visualization.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/TopLevelSelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/TopLevelParameter"
           },
           "type": "array"
         },
@@ -9268,14 +9261,7 @@
         "params": {
           "description": "An array of parameters that may either be simple variables, or more complex selections that map user input to data queries.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/SelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/SelectionParameter"
           },
           "type": "array"
         },
@@ -11092,14 +11078,7 @@
         "params": {
           "description": "An array of parameters that may either be simple variables, or more complex selections that map user input to data queries.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/SelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/SelectionParameter"
           },
           "type": "array"
         },
@@ -28440,14 +28419,7 @@
         "params": {
           "description": "Dynamic variables or selections that parameterize a visualization.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/TopLevelSelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/TopLevelParameter"
           },
           "type": "array"
         },
@@ -28584,14 +28556,7 @@
         "params": {
           "description": "Dynamic variables or selections that parameterize a visualization.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/TopLevelSelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/TopLevelParameter"
           },
           "type": "array"
         },
@@ -28714,14 +28679,7 @@
         "params": {
           "description": "Dynamic variables or selections that parameterize a visualization.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/TopLevelSelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/TopLevelParameter"
           },
           "type": "array"
         },
@@ -28872,14 +28830,7 @@
         "params": {
           "description": "Dynamic variables or selections that parameterize a visualization.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/TopLevelSelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/TopLevelParameter"
           },
           "type": "array"
         },
@@ -29045,14 +28996,7 @@
             "params": {
               "description": "Dynamic variables or selections that parameterize a visualization.",
               "items": {
-                "anyOf": [
-                  {
-                    "$ref": "#/definitions/VariableParameter"
-                  },
-                  {
-                    "$ref": "#/definitions/TopLevelSelectionParameter"
-                  }
-                ]
+                "$ref": "#/definitions/TopLevelParameter"
               },
               "type": "array"
             },
@@ -29223,14 +29167,7 @@
             "params": {
               "description": "Dynamic variables or selections that parameterize a visualization.",
               "items": {
-                "anyOf": [
-                  {
-                    "$ref": "#/definitions/VariableParameter"
-                  },
-                  {
-                    "$ref": "#/definitions/TopLevelSelectionParameter"
-                  }
-                ]
+                "$ref": "#/definitions/TopLevelParameter"
               },
               "type": "array"
             },
@@ -29411,14 +29348,7 @@
         "params": {
           "description": "Dynamic variables or selections that parameterize a visualization.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/TopLevelSelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/TopLevelParameter"
           },
           "type": "array"
         },
@@ -29478,6 +29408,16 @@
       ],
       "type": "object"
     },
+    "TopLevelParameter": {
+      "anyOf": [
+        {
+          "$ref": "#/definitions/VariableParameter"
+        },
+        {
+          "$ref": "#/definitions/TopLevelSelectionParameter"
+        }
+      ]
+    },
     "TopLevelSelectionParameter": {
       "additionalProperties": false,
       "properties": {
@@ -29711,14 +29651,7 @@
         "params": {
           "description": "An array of parameters that may either be simple variables, or more complex selections that map user input to data queries.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/SelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/TopLevelParameter"
           },
           "type": "array"
         },
@@ -30017,14 +29950,7 @@
         "params": {
           "description": "An array of parameters that may either be simple variables, or more complex selections that map user input to data queries.",
           "items": {
-            "anyOf": [
-              {
-                "$ref": "#/definitions/VariableParameter"
-              },
-              {
-                "$ref": "#/definitions/SelectionParameter"
-              }
-            ]
+            "$ref": "#/definitions/SelectionParameter"
           },
           "type": "array"
         },
diff --git a/src/normalize/index.ts b/src/normalize/index.ts
index e9423b06f7..f038a30612 100644
--- a/src/normalize/index.ts
+++ b/src/normalize/index.ts
@@ -48,7 +48,7 @@ const topLevelSelectionNormalizer = new TopLevelSelectionsNormalizer();
  * And push top-level selection definitions down to unit specs.
  */
 function normalizeGenericSpec(
-  spec: NonNormalizedSpec | FacetedUnitSpec<Field> | RepeatSpec,
+  spec: NonNormalizedSpec | FacetedUnitSpec<Field, any> | RepeatSpec,
   config: Config<SignalRef> = {}
 ) {
   const normParams = {config};
diff --git a/src/spec/toplevel.ts b/src/spec/toplevel.ts
index 690fe44daf..6a488e2b9b 100644
--- a/src/spec/toplevel.ts
+++ b/src/spec/toplevel.ts
@@ -16,6 +16,8 @@ export type Padding = number | {top?: number; bottom?: number; left?: number; ri
 
 export type Datasets = Dict<InlineDataset>;
 
+export type TopLevelParameter = VariableParameter | TopLevelSelectionParameter;
+
 export type TopLevel<S extends BaseSpec> = S &
   TopLevelProperties & {
     /**
@@ -72,7 +74,7 @@ export interface TopLevelProperties<ES extends ExprRef | SignalRef = ExprRef | S
   /**
    * Dynamic variables or selections that parameterize a visualization.
    */
-  params?: (VariableParameter | TopLevelSelectionParameter)[];
+  params?: TopLevelParameter[];
 }
 
 export type FitType = 'fit' | 'fit-x' | 'fit-y';
diff --git a/src/spec/unit.ts b/src/spec/unit.ts
index 2c3a89dc60..da69818436 100644
--- a/src/spec/unit.ts
+++ b/src/spec/unit.ts
@@ -3,16 +3,15 @@ import {CompositeEncoding, FacetedCompositeEncoding} from '../compositemark';
 import {Encoding} from '../encoding';
 import {ExprRef} from '../expr';
 import {AnyMark, Mark, MarkDef} from '../mark';
-import {VariableParameter} from '../parameter';
 import {Projection} from '../projection';
 import {SelectionParameter} from '../selection';
 import {Field} from './../channeldef';
 import {BaseSpec, DataMixins, FrameMixins, GenericCompositionLayout, ResolveMixins} from './base';
-import {TopLevel} from './toplevel';
+import {TopLevel, TopLevelParameter} from './toplevel';
 /**
  * Base interface for a unit (single-view) specification.
  */
-export interface GenericUnitSpec<E extends Encoding<any>, M> extends BaseSpec {
+export interface GenericUnitSpec<E extends Encoding<any>, M, P = SelectionParameter> extends BaseSpec {
   /**
    * A string describing the mark type (one of `"bar"`, `"circle"`, `"square"`, `"tick"`, `"line"`,
    * `"area"`, `"point"`, `"rule"`, `"geoshape"`, and `"text"`) or a [mark definition object](https://vega.github.io/vega-lite/docs/mark.html#mark-def).
@@ -33,7 +32,7 @@ export interface GenericUnitSpec<E extends Encoding<any>, M> extends BaseSpec {
   /**
    * An array of parameters that may either be simple variables, or more complex selections that map user input to data queries.
    */
-  params?: (VariableParameter | SelectionParameter)[];
+  params?: P[];
 }
 
 /**
@@ -51,12 +50,16 @@ export type UnitSpecWithFrame<F extends Field> = GenericUnitSpec<CompositeEncodi
 /**
  * Unit spec that can have a composite mark and row or column channels (shorthand for a facet spec).
  */
-export type FacetedUnitSpec<F extends Field> = GenericUnitSpec<FacetedCompositeEncoding<F>, AnyMark> &
+export type FacetedUnitSpec<F extends Field, P = SelectionParameter> = GenericUnitSpec<
+  FacetedCompositeEncoding<F>,
+  AnyMark,
+  P
+> &
   ResolveMixins &
   GenericCompositionLayout &
   FrameMixins;
 
-export type TopLevelUnitSpec<F extends Field> = TopLevel<FacetedUnitSpec<F>> & DataMixins;
+export type TopLevelUnitSpec<F extends Field> = TopLevel<FacetedUnitSpec<F, TopLevelParameter>> & DataMixins;
 
 export function isUnitSpec(spec: BaseSpec): spec is FacetedUnitSpec<any> | NormalizedUnitSpec {
   return 'mark' in spec;
diff --git a/test/compile/selection/parse.test.ts b/test/compile/selection/parse.test.ts
index 0e04759ad8..2600ebb07c 100644
--- a/test/compile/selection/parse.test.ts
+++ b/test/compile/selection/parse.test.ts
@@ -306,7 +306,7 @@ describe('Selection', () => {
           params: [
             {
               name: 'index',
-              value: {x: {year: 2005, month: 1, date: 1}},
+              value: [{x: {year: 2005, month: 1, date: 1}}],
               select: {
                 type: 'point',
                 on: 'mouseover',
diff --git a/test/compile/selection/scales.test.ts b/test/compile/selection/scales.test.ts
index 471777ea79..fc16df2144 100644
--- a/test/compile/selection/scales.test.ts
+++ b/test/compile/selection/scales.test.ts
@@ -11,13 +11,13 @@ describe('Selection + Scales', () => {
   describe('selectionExtent', () => {
     it('is assembled from selection parameter', () => {
       const model = parseConcatModel({
+        params: [{name: 'var'}],
         vconcat: [
           {
             mark: 'area',
             params: [
               {name: 'brush', select: {type: 'interval', encodings: ['x']}},
-              {name: 'brush2', select: {type: 'point', fields: ['price'], resolve: 'intersect'}},
-              {name: 'var'}
+              {name: 'brush2', select: {type: 'point', fields: ['price'], resolve: 'intersect'}}
             ],
             encoding: {
               x: {field: 'date', type: 'temporal'},