diff --git a/packages/grafana-ui/src/components/Combobox/Combobox.story.tsx b/packages/grafana-ui/src/components/Combobox/Combobox.story.tsx
index 73526a825a7..309a3028098 100644
--- a/packages/grafana-ui/src/components/Combobox/Combobox.story.tsx
+++ b/packages/grafana-ui/src/components/Combobox/Combobox.story.tsx
@@ -330,6 +330,52 @@ export const Async: StoryObj<PropsAndCustomArgs> = {
   render: AsyncStory,
 };
 
+const noop = () => {};
+const PositioningTestStory: StoryFn<PropsAndCustomArgs> = (args) => {
+  if (typeof args.options === 'function') {
+    throw new Error('This story does not support async options');
+  }
+
+  function renderColumnOfComboboxes(pos: string) {
+    return (
+      <div
+        style={{
+          display: 'flex',
+          flexDirection: 'column',
+          justifyContent: 'space-between',
+          flex: 1,
+        }}
+      >
+        <Combobox placeholder={`${pos} top`} options={args.options} value={null} onChange={noop} />
+        <Combobox placeholder={`${pos} middle`} options={args.options} value={null} onChange={noop} />
+        <Combobox placeholder={`${pos} bottom`} options={args.options} value={null} onChange={noop} />
+      </div>
+    );
+  }
+
+  return (
+    <div
+      style={{
+        display: 'flex',
+        flexDirection: 'row',
+
+        // approx the height of the dev alert, and three margins. exact doesn't matter
+        minHeight: 'calc(100vh - (105px + 16px + 16px + 16px))',
+        justifyContent: 'space-between',
+        gap: 32,
+      }}
+    >
+      {renderColumnOfComboboxes('Left')}
+      {renderColumnOfComboboxes('Middle')}
+      {renderColumnOfComboboxes('Right')}
+    </div>
+  );
+};
+
+export const PositioningTest: StoryObj<PropsAndCustomArgs> = {
+  render: PositioningTestStory,
+};
+
 export const ComparisonToSelect: StoryObj<PropsAndCustomArgs> = {
   args: {
     numberOfOptions: 100,
diff --git a/packages/grafana-ui/src/components/Combobox/Combobox.tsx b/packages/grafana-ui/src/components/Combobox/Combobox.tsx
index 6813b634318..ec402f78dc1 100644
--- a/packages/grafana-ui/src/components/Combobox/Combobox.tsx
+++ b/packages/grafana-ui/src/components/Combobox/Combobox.tsx
@@ -10,7 +10,7 @@ import { AutoSizeInput } from '../Input/AutoSizeInput';
 import { Input, Props as InputProps } from '../Input/Input';
 
 import { getComboboxStyles } from './getComboboxStyles';
-import { estimateSize, useComboboxFloat } from './useComboboxFloat';
+import { useComboboxFloat, OPTION_HEIGHT } from './useComboboxFloat';
 import { StaleResultError, useLatestAsyncCall } from './useLatestAsyncCall';
 
 export type ComboboxOption<T extends string | number = string> = {
@@ -129,7 +129,7 @@ export const Combobox = <T extends string | number>({
   const virtualizerOptions = {
     count: items.length,
     getScrollElement: () => floatingRef.current,
-    estimateSize,
+    estimateSize: () => OPTION_HEIGHT,
     overscan: 4,
   };
 
diff --git a/packages/grafana-ui/src/components/Combobox/getComboboxStyles.ts b/packages/grafana-ui/src/components/Combobox/getComboboxStyles.ts
index e967c260f85..9c24efae0ea 100644
--- a/packages/grafana-ui/src/components/Combobox/getComboboxStyles.ts
+++ b/packages/grafana-ui/src/components/Combobox/getComboboxStyles.ts
@@ -2,8 +2,6 @@ import { css } from '@emotion/css';
 
 import { GrafanaTheme2 } from '@grafana/data';
 
-const MAX_HEIGHT = 400;
-
 // We need a px font size to accurately measure the width of items.
 // This should be in sync with the body font size in the theme.
 export const MENU_ITEM_FONT_SIZE = 14;
@@ -20,7 +18,6 @@ export const getComboboxStyles = (theme: GrafanaTheme2) => {
       background: theme.components.dropdown.background,
       boxShadow: theme.shadows.z3,
       zIndex: theme.zIndex.dropdown,
-      maxHeight: MAX_HEIGHT,
       overflowY: 'auto',
       position: 'relative',
     }),
diff --git a/packages/grafana-ui/src/components/Combobox/useComboboxFloat.ts b/packages/grafana-ui/src/components/Combobox/useComboboxFloat.ts
index 0dc912f29e4..6b271d081ed 100644
--- a/packages/grafana-ui/src/components/Combobox/useComboboxFloat.ts
+++ b/packages/grafana-ui/src/components/Combobox/useComboboxFloat.ts
@@ -9,12 +9,12 @@ import { MENU_ITEM_FONT_SIZE, MENU_ITEM_FONT_WEIGHT, MENU_ITEM_PADDING_X } from
 // Only consider the first n items when calculating the width of the popover.
 const WIDTH_CALCULATION_LIMIT_ITEMS = 100_000;
 
-/**
- * Used with Downshift to get the height of each item
- */
-export function estimateSize() {
-  return 45;
-}
+// Used with Downshift to get the height of each item
+export const OPTION_HEIGHT = 45;
+const POPOVER_MAX_HEIGHT = OPTION_HEIGHT * 8.5;
+
+// Clearance around the popover to prevent it from being too close to the edge of the viewport
+const POPOVER_PADDING = 16;
 
 export const useComboboxFloat = (
   items: Array<ComboboxOption<string | number>>,
@@ -23,7 +23,7 @@ export const useComboboxFloat = (
 ) => {
   const inputRef = useRef<HTMLInputElement>(null);
   const floatingRef = useRef<HTMLDivElement>(null);
-  const [popoverMaxWidth, setPopoverMaxWidth] = useState<number | undefined>(undefined);
+  const [popoverMaxSize, setPopoverMaxSize] = useState<{ width: number; height: number } | undefined>(undefined);
 
   const scrollbarWidth = useMemo(() => getScrollbarWidth(), []);
 
@@ -35,8 +35,14 @@ export const useComboboxFloat = (
       boundary: document.body,
     }),
     size({
-      apply({ availableWidth }) {
-        setPopoverMaxWidth(availableWidth);
+      apply({ availableWidth, availableHeight }) {
+        const preferredMaxWidth = availableWidth - POPOVER_PADDING;
+        const preferredMaxHeight = availableHeight - POPOVER_PADDING;
+
+        const width = Math.max(preferredMaxWidth, 0);
+        const height = Math.min(Math.max(preferredMaxHeight, OPTION_HEIGHT), POPOVER_MAX_HEIGHT);
+
+        setPopoverMaxSize({ width, height });
       },
     }),
   ];
@@ -67,8 +73,10 @@ export const useComboboxFloat = (
   const floatStyles = {
     ...floatingStyles,
     width: longestItemWidth,
-    maxWidth: popoverMaxWidth,
+    maxWidth: popoverMaxSize?.width,
     minWidth: inputRef.current?.offsetWidth,
+
+    maxHeight: popoverMaxSize?.height,
   };
 
   return { inputRef, floatingRef, floatStyles };