diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7f909b3a25de..32dc8876f5f7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -41,6 +41,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Revert change that only listened for stdin close on TTYs ([#9331](https://github.com/tailwindlabs/tailwindcss/pull/9331))
 - Ignore unset values (like `null` or `undefined`) when resolving the classList for intellisense ([#9385](https://github.com/tailwindlabs/tailwindcss/pull/9385))
 - Implement fallback plugins when arbitrary values result in css from multiple plugins ([#9376](https://github.com/tailwindlabs/tailwindcss/pull/9376))
+- Improve type checking for formal syntax ([#9349](https://github.com/tailwindlabs/tailwindcss/pull/9349), [#9448](https://github.com/tailwindlabs/tailwindcss/pull/9448))
 
 ## [3.1.8] - 2022-08-05
 
diff --git a/src/corePlugins.js b/src/corePlugins.js
index 3fd4ed99c51a..5cf27287128e 100644
--- a/src/corePlugins.js
+++ b/src/corePlugins.js
@@ -1482,7 +1482,7 @@ export let corePlugins = {
   },
 
   backgroundSize: createUtilityPlugin('backgroundSize', [['bg', ['background-size']]], {
-    type: ['lookup', ['length', { preferOnConflict: true }], 'percentage'],
+    type: ['lookup', 'length', 'percentage', 'size'],
   }),
 
   backgroundAttachment: ({ addUtilities }) => {
@@ -1503,7 +1503,7 @@ export let corePlugins = {
   },
 
   backgroundPosition: createUtilityPlugin('backgroundPosition', [['bg', ['background-position']]], {
-    type: ['lookup', 'position'],
+    type: ['lookup', ['position', { preferOnConflict: true }]],
   }),
 
   backgroundRepeat: ({ addUtilities }) => {
diff --git a/src/util/dataTypes.js b/src/util/dataTypes.js
index d7f04f7044bc..beb4cec89499 100644
--- a/src/util/dataTypes.js
+++ b/src/util/dataTypes.js
@@ -6,6 +6,10 @@ let cssFunctions = ['min', 'max', 'clamp', 'calc']
 
 // Ref: https://developer.mozilla.org/en-US/docs/Web/CSS/CSS_Types
 
+function isCSSFunction(value) {
+  return cssFunctions.some((fn) => new RegExp(`^${fn}\\(.*\\)`).test(value))
+}
+
 // This is not a data type, but rather a function that can normalize the
 // correct values.
 export function normalize(value, isRoot = true) {
@@ -55,13 +59,11 @@ export function url(value) {
 }
 
 export function number(value) {
-  return !isNaN(Number(value)) || cssFunctions.some((fn) => new RegExp(`^${fn}\\(.+?`).test(value))
+  return !isNaN(Number(value)) || isCSSFunction(value)
 }
 
 export function percentage(value) {
-  return splitAtTopLevelOnly(value, '_').every((part) => {
-    return /%$/g.test(part) || cssFunctions.some((fn) => new RegExp(`^${fn}\\(.+?%`).test(part))
-  })
+  return (value.endsWith('%') && number(value.slice(0, -1))) || isCSSFunction(value)
 }
 
 let lengthUnits = [
@@ -84,13 +86,11 @@ let lengthUnits = [
 ]
 let lengthUnitsPattern = `(?:${lengthUnits.join('|')})`
 export function length(value) {
-  return splitAtTopLevelOnly(value, '_').every((part) => {
-    return (
-      part === '0' ||
-      new RegExp(`${lengthUnitsPattern}$`).test(part) ||
-      cssFunctions.some((fn) => new RegExp(`^${fn}\\(.+?${lengthUnitsPattern}`).test(part))
-    )
-  })
+  return (
+    value === '0' ||
+    new RegExp(`^[+-]?[0-9]*\.?[0-9]+(?:[eE][+-]?[0-9]+)?${lengthUnitsPattern}$`).test(value) ||
+    isCSSFunction(value)
+  )
 }
 
 let lineWidths = new Set(['thin', 'medium', 'thick'])
diff --git a/src/util/pluginUtils.js b/src/util/pluginUtils.js
index d056a78cee01..c56f6a1dd412 100644
--- a/src/util/pluginUtils.js
+++ b/src/util/pluginUtils.js
@@ -18,6 +18,7 @@ import {
   shadow,
 } from './dataTypes'
 import negateValue from './negateValue'
+import { backgroundSize } from './validateFormalSyntax'
 
 export function updateAllClasses(selectors, updateClass) {
   let parser = selectorParser((selectors) => {
@@ -162,6 +163,7 @@ export let typeMap = {
   'absolute-size': guess(absoluteSize),
   'relative-size': guess(relativeSize),
   shadow: guess(shadow),
+  size: guess(backgroundSize),
 }
 
 let supportedTypes = Object.keys(typeMap)
diff --git a/src/util/validateFormalSyntax.js b/src/util/validateFormalSyntax.js
new file mode 100644
index 000000000000..d3dafea1f07f
--- /dev/null
+++ b/src/util/validateFormalSyntax.js
@@ -0,0 +1,34 @@
+import { length, percentage } from './dataTypes'
+import { splitAtTopLevelOnly } from './splitAtTopLevelOnly'
+
+/**
+ *
+ * https://developer.mozilla.org/en-US/docs/Web/CSS/background-size#formal_syntax
+ *
+ * background-size =
+ *  <bg-size>#
+ *
+ * <bg-size> =
+ *   [ <length-percentage [0,∞]> | auto ]{1,2}  |
+ *   cover                                      |
+ *   contain
+ *
+ * <length-percentage> =
+ *   <length>      |
+ *   <percentage>
+ *
+ * @param {string} value
+ */
+export function backgroundSize(value) {
+  let keywordValues = ['cover', 'contain']
+  // the <length-percentage> type will probably be a css function
+  // so we have to use `splitAtTopLevelOnly`
+  return splitAtTopLevelOnly(value, ',').every((part) => {
+    let sizes = splitAtTopLevelOnly(part, '_').filter(Boolean)
+    if (sizes.length === 1 && keywordValues.includes(sizes[0])) return true
+
+    if (sizes.length !== 1 && sizes.length !== 2) return false
+
+    return sizes.every((size) => length(size) || percentage(size) || size === 'auto')
+  })
+}
diff --git a/tests/arbitrary-values.test.js b/tests/arbitrary-values.test.js
index a4dbf6fe990a..da17a6cdf1aa 100644
--- a/tests/arbitrary-values.test.js
+++ b/tests/arbitrary-values.test.js
@@ -285,7 +285,7 @@ it('should pick the fallback plugin when arbitrary values collide', () => {
       }
 
       .bg-\[200px_100px\] {
-        background-size: 200px 100px;
+        background-position: 200px 100px;
       }
     `)
   })
@@ -311,7 +311,7 @@ it('should warn and not generate if arbitrary values are ambiguous (without fall
     plugins: [
       function ({ matchUtilities }) {
         matchUtilities({ foo: (value) => ({ value }) }, { type: ['position'] })
-        matchUtilities({ foo: (value) => ({ value }) }, { type: ['length'] })
+        matchUtilities({ foo: (value) => ({ value }) }, { type: ['size'] })
       },
     ],
   }
@@ -463,3 +463,77 @@ it('should correctly validate each part when checking for `percentage` data type
     `)
   })
 })
+
+it('should correctly validate background size', () => {
+  let config = {
+    content: [{ raw: html`<div class="bg-[auto_auto,cover,_contain,10px,10px_10%]"></div>` }],
+    corePlugins: { preflight: false },
+    plugins: [],
+  }
+
+  let input = css`
+    @tailwind utilities;
+  `
+
+  return run(input, config).then((result) => {
+    expect(result.css).toMatchFormattedCss(css`
+      .bg-\[auto_auto\2c cover\2c _contain\2c 10px\2c 10px_10\%\] {
+        background-size: auto auto, cover, contain, 10px, 10px 10%;
+      }
+    `)
+  })
+})
+
+it('should correctly validate combination of percentage and length', () => {
+  let config = {
+    content: [{ raw: html`<div class="bg-[50px_10%] bg-[50%_10%] bg-[50px_10px]"></div>` }],
+    corePlugins: { preflight: false },
+    plugins: [],
+  }
+
+  let input = css`
+    @tailwind utilities;
+  `
+
+  return run(input, config).then((result) => {
+    expect(result.css).toMatchFormattedCss(css`
+      .bg-\[50px_10\%\] {
+        background-position: 50px 10%;
+      }
+      .bg-\[50\%_10\%\] {
+        background-position: 50% 10%;
+      }
+      .bg-\[50px_10px\] {
+        background-position: 50px 10px;
+      }
+    `)
+  })
+})
+
+it('can explicitly specify type for percentage and length', () => {
+  let config = {
+    content: [
+      { raw: html`<div class="bg-[size:50px_10%] bg-[50px_10px] bg-[position:50%_10%]"></div>` },
+    ],
+    corePlugins: { preflight: false },
+    plugins: [],
+  }
+
+  let input = css`
+    @tailwind utilities;
+  `
+
+  return run(input, config).then((result) => {
+    expect(result.css).toMatchFormattedCss(css`
+      .bg-\[size\:50px_10\%\] {
+        background-size: 50px 10%;
+      }
+      .bg-\[50px_10px\] {
+        background-position: 50px 10px;
+      }
+      .bg-\[position\:50\%_10\%\] {
+        background-position: 50% 10%;
+      }
+    `)
+  })
+})