diff --git a/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.test.tsx b/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.test.tsx
index f649564b2231a..083ceff3bb444 100644
--- a/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.test.tsx
+++ b/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.test.tsx
@@ -176,5 +176,39 @@ describe('Datatable Visualization', () => {
         ],
       });
     });
+
+    it('reorders the rendered colums based on the order from the datasource', () => {
+      const datasource = createMockDatasource();
+      const layer = { layerId: 'a', columns: ['b', 'c'] };
+      const frame = mockFrame();
+      frame.datasourceLayers = { a: datasource.publicAPIMock };
+      const component = mount(
+        <DataTableLayer
+          dragDropContext={{ dragging: undefined, setDragging: () => {} }}
+          frame={frame}
+          layer={layer}
+          setState={jest.fn()}
+          state={{ layers: [layer] }}
+        />
+      );
+
+      const accessors = component
+        .find('[data-test-subj="datatable_multicolumnEditor"]')
+        .first()
+        .prop('accessors') as string[];
+
+      expect(accessors).toEqual(['b', 'c']);
+
+      component.setProps({
+        layer: { layerId: 'a', columns: ['c', 'b'] },
+      });
+
+      const newAccessors = component
+        .find('[data-test-subj="datatable_multicolumnEditor"]')
+        .first()
+        .prop('accessors') as string[];
+
+      expect(newAccessors).toEqual(['c', 'b']);
+    });
   });
 });
diff --git a/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.tsx b/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.tsx
index 18a6d112e14d6..31d2e6ad4c7a4 100644
--- a/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.tsx
+++ b/x-pack/legacy/plugins/lens/public/datatable_visualization_plugin/visualization.tsx
@@ -58,6 +58,11 @@ export function DataTableLayer({
   dragDropContext,
 }: { layer: LayerState } & VisualizationProps<DatatableVisualizationState>) {
   const datasource = frame.datasourceLayers[layer.layerId];
+
+  const originalOrder = datasource.getTableSpec().map(({ columnId }) => columnId);
+  // When we add a column it could be empty, and therefore have no order
+  const sortedColumns = Array.from(new Set(originalOrder.concat(layer.columns)));
+
   return (
     <EuiPanel className="lnsConfigPanel__panel" paddingSize="s">
       <NativeRenderer
@@ -71,7 +76,7 @@ export function DataTableLayer({
         label={i18n.translate('xpack.lens.datatable.columns', { defaultMessage: 'Columns' })}
       >
         <MultiColumnEditor
-          accessors={layer.columns}
+          accessors={sortedColumns}
           datasource={datasource}
           dragDropContext={dragDropContext}
           filterOperations={allOperations}
diff --git a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.test.tsx b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.test.tsx
index c9d7ce1ea81f8..c6dbb6f617acf 100644
--- a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.test.tsx
+++ b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.test.tsx
@@ -29,7 +29,7 @@ describe('BucketNestingEditor', () => {
     return result as IndexPatternColumn;
   }
 
-  it('should display an unchecked switch if there are two buckets and it is the root', () => {
+  it('should display the top level grouping when at the root', () => {
     const component = mount(
       <BucketNestingEditor
         columnId="a"
@@ -45,12 +45,14 @@ describe('BucketNestingEditor', () => {
         setColumns={jest.fn()}
       />
     );
-    const control = component.find('[data-test-subj="indexPattern-nesting-switch"]').first();
+    const control1 = component.find('[data-test-subj="indexPattern-nesting-topLevel"]').first();
+    const control2 = component.find('[data-test-subj="indexPattern-nesting-bottomLevel"]').first();
 
-    expect(control.prop('checked')).toBeFalsy();
+    expect(control1.prop('checked')).toBeTruthy();
+    expect(control2.prop('checked')).toBeFalsy();
   });
 
-  it('should display a checked switch if there are two buckets and it is not the root', () => {
+  it('should display the bottom level grouping when appropriate', () => {
     const component = mount(
       <BucketNestingEditor
         columnId="a"
@@ -66,9 +68,12 @@ describe('BucketNestingEditor', () => {
         setColumns={jest.fn()}
       />
     );
-    const control = component.find('[data-test-subj="indexPattern-nesting-switch"]').first();
 
-    expect(control.prop('checked')).toBeTruthy();
+    const control1 = component.find('[data-test-subj="indexPattern-nesting-topLevel"]').first();
+    const control2 = component.find('[data-test-subj="indexPattern-nesting-bottomLevel"]').first();
+
+    expect(control1.prop('checked')).toBeFalsy();
+    expect(control2.prop('checked')).toBeTruthy();
   });
 
   it('should reorder the columns when toggled', () => {
@@ -88,11 +93,31 @@ describe('BucketNestingEditor', () => {
         setColumns={setColumns}
       />
     );
-    const control = component.find('[data-test-subj="indexPattern-nesting-switch"]').first();
+    const control1 = component.find('[data-test-subj="indexPattern-nesting-topLevel"]').first();
 
-    (control.prop('onChange') as () => {})();
+    (control1.prop('onChange') as () => {})();
 
+    expect(setColumns).toHaveBeenCalledTimes(1);
     expect(setColumns).toHaveBeenCalledWith(['a', 'b', 'c']);
+
+    component.setProps({
+      layer: {
+        columnOrder: ['a', 'b', 'c'],
+        columns: {
+          a: mockCol({ suggestedPriority: 0 }),
+          b: mockCol({ suggestedPriority: 1 }),
+          c: mockCol({ suggestedPriority: 2, operationType: 'min', isBucketed: false }),
+        },
+        indexPatternId: 'foo',
+      },
+    });
+
+    const control2 = component.find('[data-test-subj="indexPattern-nesting-bottomLevel"]').first();
+
+    (control2.prop('onChange') as () => {})();
+
+    expect(setColumns).toHaveBeenCalledTimes(2);
+    expect(setColumns).toHaveBeenLastCalledWith(['b', 'a', 'c']);
   });
 
   it('should display nothing if there are no buckets', () => {
diff --git a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.tsx b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.tsx
index 71f5722151802..04e13fead6fca 100644
--- a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.tsx
+++ b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/bucket_nesting_editor.tsx
@@ -7,8 +7,11 @@
 import _ from 'lodash';
 import React from 'react';
 import { i18n } from '@kbn/i18n';
-import { EuiFormRow, EuiHorizontalRule, EuiSwitch, EuiSelect } from '@elastic/eui';
+import { EuiFormRow, EuiHorizontalRule, EuiRadio, EuiSelect, htmlIdGenerator } from '@elastic/eui';
 import { IndexPatternLayer } from '../types';
+import { hasField } from '../utils';
+
+const generator = htmlIdGenerator('lens-nesting');
 
 function nestColumn(columnOrder: string[], outer: string, inner: string) {
   const result = columnOrder.filter(c => c !== inner);
@@ -32,35 +35,75 @@ export function BucketNestingEditor({
   const columns = Object.entries(layer.columns);
   const aggColumns = columns
     .filter(([id, c]) => id !== columnId && c.isBucketed)
-    .map(([value, c]) => ({ value, text: c.label }));
+    .map(([value, c]) => ({
+      value,
+      text: c.label,
+      fieldName: hasField(c) ? c.sourceField : '',
+    }));
 
   if (!column || !column.isBucketed || !aggColumns.length) {
     return null;
   }
 
+  const fieldName = hasField(column) ? column.sourceField : '';
+
   const prevColumn = layer.columnOrder[layer.columnOrder.indexOf(columnId) - 1];
 
   if (aggColumns.length === 1) {
     const [target] = aggColumns;
 
+    function toggleNesting() {
+      if (prevColumn) {
+        setColumns(nestColumn(layer.columnOrder, columnId, target.value));
+      } else {
+        setColumns(nestColumn(layer.columnOrder, target.value, columnId));
+      }
+    }
+
     return (
       <>
         <EuiHorizontalRule margin="m" />
-        <EuiSwitch
-          data-test-subj="indexPattern-nesting-switch"
-          label={i18n.translate('xpack.lens.xyChart.nestUnderTarget', {
-            defaultMessage: 'Nest under {target}',
-            values: { target: target.text },
+        <EuiFormRow
+          label={i18n.translate('xpack.lens.indexPattern.groupingControlLabel', {
+            defaultMessage: 'Grouping',
           })}
-          checked={!!prevColumn}
-          onChange={() => {
-            if (prevColumn) {
-              setColumns(nestColumn(layer.columnOrder, columnId, target.value));
-            } else {
-              setColumns(nestColumn(layer.columnOrder, target.value, columnId));
-            }
-          }}
-        />
+        >
+          <>
+            <EuiRadio
+              id={generator('topLevel')}
+              data-test-subj="indexPattern-nesting-topLevel"
+              label={
+                column.operationType === 'terms'
+                  ? i18n.translate('xpack.lens.indexPattern.groupingOverallTerms', {
+                      defaultMessage: 'Overall top {field}',
+                      values: { field: fieldName },
+                    })
+                  : i18n.translate('xpack.lens.indexPattern.groupingOverallDateHistogram', {
+                      defaultMessage: 'Dates overall',
+                    })
+              }
+              checked={!prevColumn}
+              onChange={toggleNesting}
+            />
+            <EuiRadio
+              id={generator('bottomLevel')}
+              data-test-subj="indexPattern-nesting-bottomLevel"
+              label={
+                column.operationType === 'terms'
+                  ? i18n.translate('xpack.lens.indexPattern.groupingSecondTerms', {
+                      defaultMessage: 'Top values for each {target}',
+                      values: { target: target.fieldName },
+                    })
+                  : i18n.translate('xpack.lens.indexPattern.groupingSecondDateHistogram', {
+                      defaultMessage: 'Dates for each {target}',
+                      values: { target: target.fieldName },
+                    })
+              }
+              checked={!!prevColumn}
+              onChange={toggleNesting}
+            />
+          </>
+        </EuiFormRow>
       </>
     );
   }
@@ -69,8 +112,8 @@ export function BucketNestingEditor({
     <>
       <EuiHorizontalRule margin="m" />
       <EuiFormRow
-        label={i18n.translate('xpack.lens.xyChart.nestUnder', {
-          defaultMessage: 'Nest under',
+        label={i18n.translate('xpack.lens.indexPattern.groupByDropdown', {
+          defaultMessage: 'Group by',
         })}
         display="rowCompressed"
       >
@@ -81,7 +124,7 @@ export function BucketNestingEditor({
             {
               value: '',
               text: i18n.translate('xpack.lens.xyChart.nestUnderRoot', {
-                defaultMessage: 'Top level',
+                defaultMessage: 'Entire data set',
               }),
             },
             ...aggColumns,
diff --git a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/popover_editor.tsx b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/popover_editor.tsx
index bc46143b5f3b5..b9baa489f3382 100644
--- a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/popover_editor.tsx
+++ b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/dimension_panel/popover_editor.tsx
@@ -70,6 +70,7 @@ export function PopoverEditor(props: PopoverEditorProps) {
     layerId,
     currentIndexPattern,
     uniqueLabel,
+    hideGrouping,
   } = props;
   const { operationByDocument, operationByField, fieldByOperation } = operationFieldSupportMatrix;
   const [isPopoverOpen, setPopoverOpen] = useState(false);
@@ -399,22 +400,25 @@ export function PopoverEditor(props: PopoverEditorProps) {
                     />
                   </EuiFormRow>
                 )}
-                <BucketNestingEditor
-                  layer={state.layers[props.layerId]}
-                  columnId={props.columnId}
-                  setColumns={columnOrder => {
-                    setState({
-                      ...state,
-                      layers: {
-                        ...state.layers,
-                        [props.layerId]: {
-                          ...state.layers[props.layerId],
-                          columnOrder,
+
+                {!hideGrouping && (
+                  <BucketNestingEditor
+                    layer={state.layers[props.layerId]}
+                    columnId={props.columnId}
+                    setColumns={columnOrder => {
+                      setState({
+                        ...state,
+                        layers: {
+                          ...state.layers,
+                          [props.layerId]: {
+                            ...state.layers[props.layerId],
+                            columnOrder,
+                          },
                         },
-                      },
-                    });
-                  }}
-                />
+                      });
+                    }}
+                  />
+                )}
               </EuiFlexItem>
             </EuiFlexGroup>
           </EuiFlexItem>
diff --git a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/indexpattern_suggestions.ts b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/indexpattern_suggestions.ts
index f3e4c32103abf..49944614edbb4 100644
--- a/x-pack/legacy/plugins/lens/public/indexpattern_plugin/indexpattern_suggestions.ts
+++ b/x-pack/legacy/plugins/lens/public/indexpattern_plugin/indexpattern_suggestions.ts
@@ -460,9 +460,9 @@ function createMetricSuggestion(
 
 function getNestedTitle([outerBucket, innerBucket]: IndexPatternColumn[]) {
   return i18n.translate('xpack.lens.indexpattern.suggestions.nestingChangeLabel', {
-    defaultMessage: '{innerOperation} per each {outerOperation}',
+    defaultMessage: '{innerOperation} for each {outerOperation}',
     values: {
-      innerOperation: innerBucket.label,
+      innerOperation: hasField(innerBucket) ? innerBucket.sourceField : innerBucket.label,
       outerOperation: hasField(outerBucket) ? outerBucket.sourceField : outerBucket.label,
     },
   });
diff --git a/x-pack/legacy/plugins/lens/public/types.ts b/x-pack/legacy/plugins/lens/public/types.ts
index 2713a44f53980..1efa123f4f0a3 100644
--- a/x-pack/legacy/plugins/lens/public/types.ts
+++ b/x-pack/legacy/plugins/lens/public/types.ts
@@ -189,6 +189,11 @@ export interface DatasourceDimensionPanelProps {
   // affects the default ordering of the query
   suggestedPriority?: DimensionPriority;
   onRemove?: (accessor: string) => void;
+
+  // Some dimension editors will allow users to change the operation grouping
+  // from the panel, and this lets the visualization hint that it doesn't want
+  // users to have that level of control
+  hideGrouping?: boolean;
 }
 
 export interface DatasourceLayerPanelProps {
diff --git a/x-pack/legacy/plugins/lens/public/xy_visualization_plugin/xy_config_panel.tsx b/x-pack/legacy/plugins/lens/public/xy_visualization_plugin/xy_config_panel.tsx
index 9461229313f4c..322e1f1ea4a0e 100644
--- a/x-pack/legacy/plugins/lens/public/xy_visualization_plugin/xy_config_panel.tsx
+++ b/x-pack/legacy/plugins/lens/public/xy_visualization_plugin/xy_config_panel.tsx
@@ -186,6 +186,7 @@ export function XYConfigPanel(props: VisualizationProps<State>) {
                 filterOperations: isBucketed,
                 suggestedPriority: 1,
                 layerId: layer.layerId,
+                hideGrouping: true,
               }}
             />
           </EuiFormRow>