diff --git a/src/vs/workbench/contrib/notebook/browser/media/notebook.css b/src/vs/workbench/contrib/notebook/browser/media/notebook.css
index 4ed5411e1b86e176106c6cd7efa734e3f9df3177..92c2562b6572908a7fffe1c36eaf3fc94ede401d 100644
--- a/src/vs/workbench/contrib/notebook/browser/media/notebook.css
+++ b/src/vs/workbench/contrib/notebook/browser/media/notebook.css
@@ -464,12 +464,6 @@
 	cursor: pointer;
 }
 
-.monaco-workbench .notebookOverlay .monaco-list .monaco-list-row:hover .cell-focus-indicator,
-.monaco-workbench .notebookOverlay .monaco-list .monaco-list-row.cell-output-hover .cell-focus-indicator,
-.monaco-workbench .notebookOverlay .monaco-list .monaco-list-row.focused .cell-focus-indicator {
-	opacity: 1;
-}
-
 .monaco-workbench .notebookOverlay .monaco-list-row .cell-editor-part:before {
 	z-index: 20;
 	content: "";
diff --git a/src/vs/workbench/contrib/notebook/browser/notebookEditorWidget.ts b/src/vs/workbench/contrib/notebook/browser/notebookEditorWidget.ts
index 45a1efd95aadc95f99ad6f88f1eac3a2e72e5f5f..df4e7d2e45d5fb4a881a31fe4aadceece8d2553b 100644
--- a/src/vs/workbench/contrib/notebook/browser/notebookEditorWidget.ts
+++ b/src/vs/workbench/contrib/notebook/browser/notebookEditorWidget.ts
@@ -1200,7 +1200,7 @@ export class NotebookEditorWidget extends Disposable implements INotebookEditor
 			return null;
 		}
 
-		const newIdx = index + 1;
+		const newIdx = index + 2; // This is the adjustment for the index before the cell has been "removed" from its original index
 		return this._moveCellToIndex(index, newIdx);
 	}
 
@@ -1231,10 +1231,6 @@ export class NotebookEditorWidget extends Disposable implements INotebookEditor
 		const relativeToIndex = this._notebookViewModel!.getCellIndex(relativeToCell);
 
 		let newIdx = direction === 'above' ? relativeToIndex : relativeToIndex + 1;
-		if (originalIdx < newIdx) {
-			newIdx--;
-		}
-
 		return this._moveCellToIndex(originalIdx, newIdx);
 	}
 
@@ -1247,7 +1243,17 @@ export class NotebookEditorWidget extends Disposable implements INotebookEditor
 		return this._moveCellToIndex(originalIdx, index);
 	}
 
+	/**
+	 * @param index The current index of the cell
+	 * @param newIdx The desired index, in an index scheme for the state of the tree before the current cell has been "removed".
+	 * @example to move the cell from index 0 down one spot, call with (0, 2)
+	 */
 	private async _moveCellToIndex(index: number, newIdx: number): Promise<ICellViewModel | null> {
+		if (index < newIdx) {
+			// The cell is moving "down", it will free up one index spot and consume a new one
+			newIdx--;
+		}
+
 		if (index === newIdx) {
 			return null;
 		}
diff --git a/src/vs/workbench/contrib/notebook/browser/view/renderers/cellRenderer.ts b/src/vs/workbench/contrib/notebook/browser/view/renderers/cellRenderer.ts
index 1cf2b75d684c636aecfbb802a49faed9fae87213..d0b8d958d687d4b81265c8930486ebd28903f6d9 100644
--- a/src/vs/workbench/contrib/notebook/browser/view/renderers/cellRenderer.ts
+++ b/src/vs/workbench/contrib/notebook/browser/view/renderers/cellRenderer.ts
@@ -622,9 +622,9 @@ export class CellDragAndDropController extends Disposable {
 
 		const dropDirection = this.getDropInsertDirection(event);
 		const insertionIndicatorAbsolutePos = dropDirection === 'above' ? event.cellTop : event.cellTop + event.cellHeight;
-		const insertionIndicatorTop = insertionIndicatorAbsolutePos - this.list.scrollTop;
+		const insertionIndicatorTop = insertionIndicatorAbsolutePos - this.list.scrollTop + BOTTOM_CELL_TOOLBAR_HEIGHT / 2;
 		if (insertionIndicatorTop >= 0) {
-			this.listInsertionIndicator.style.top = `${insertionIndicatorAbsolutePos - this.list.scrollTop}px`;
+			this.listInsertionIndicator.style.top = `${insertionIndicatorTop}px`;
 			this.setInsertIndicatorVisibility(true);
 		} else {
 			this.setInsertIndicatorVisibility(false);
@@ -637,6 +637,11 @@ export class CellDragAndDropController extends Disposable {
 
 	private onCellDrop(event: CellDragEvent): void {
 		const draggedCell = this.currentDraggedCell!;
+
+		if (this.isScrolling || this.currentDraggedCell === event.draggedOverCell) {
+			return;
+		}
+
 		let draggedCells: ICellViewModel[] = [draggedCell];
 
 		if (draggedCell.cellKind === CellKind.Markdown) {
@@ -655,7 +660,7 @@ export class CellDragAndDropController extends Disposable {
 
 		const dropDirection = this.getDropInsertDirection(event);
 		const insertionIndicatorAbsolutePos = dropDirection === 'above' ? event.cellTop : event.cellTop + event.cellHeight;
-		const insertionIndicatorTop = insertionIndicatorAbsolutePos - this.list.scrollTop;
+		const insertionIndicatorTop = insertionIndicatorAbsolutePos - this.list.scrollTop + BOTTOM_CELL_TOOLBAR_HEIGHT / 2;
 		const editorHeight = this.notebookEditor.getDomNode().getBoundingClientRect().height;
 		if (insertionIndicatorTop < 0 || insertionIndicatorTop > editorHeight) {
 			// Ignore drop, insertion point is off-screen