diff --git a/packages/blocks/src/api/index.js b/packages/blocks/src/api/index.js
index d9fb8f5668964a..0bdf1d01abd6be 100644
--- a/packages/blocks/src/api/index.js
+++ b/packages/blocks/src/api/index.js
@@ -11,7 +11,7 @@ export {
 	getBlockAttributes,
 	parseWithAttributeSchema,
 } from './parser';
-export { default as rawHandler, getPhrasingContentSchema } from './raw-handling';
+export { pasteHandler, rawHandler, getPhrasingContentSchema } from './raw-handling';
 export {
 	default as serialize,
 	getBlockContent,
diff --git a/packages/blocks/src/api/raw-handling/index.js b/packages/blocks/src/api/raw-handling/index.js
index 82488e70380776..c38cdab46e0dcc 100644
--- a/packages/blocks/src/api/raw-handling/index.js
+++ b/packages/blocks/src/api/raw-handling/index.js
@@ -65,6 +65,51 @@ function getRawTransformations() {
 		} );
 }
 
+/**
+ * Converts HTML directly to blocks. Looks for a matching transform for each
+ * top-level tag. The HTML should be filtered to not have any text between
+ * top-level tags and formatted in a way that blocks can handle the HTML.
+ *
+ * @param  {Object} $1               Named parameters.
+ * @param  {string} $1.html          HTML to convert.
+ * @param  {Array}  $1.rawTransforms Transforms that can be used.
+ *
+ * @return {Array} An array of blocks.
+ */
+function htmlToBlocks( { html, rawTransforms } ) {
+	const doc = document.implementation.createHTMLDocument( '' );
+
+	doc.body.innerHTML = html;
+
+	return Array.from( doc.body.children ).map( ( node ) => {
+		const rawTransform = findTransform( rawTransforms, ( { isMatch } ) => isMatch( node ) );
+
+		if ( ! rawTransform ) {
+			console.warn(
+				'A block registered a raw transformation schema for `' + node.nodeName + '` but did not match it. ' +
+				'Make sure there is a `selector` or `isMatch` property that can match the schema.\n' +
+				'Sanitized HTML: `' + node.outerHTML + '`'
+			);
+
+			return;
+		}
+
+		const { transform, blockName } = rawTransform;
+
+		if ( transform ) {
+			return transform( node );
+		}
+
+		return createBlock(
+			blockName,
+			getBlockAttributes(
+				getBlockType( blockName ),
+				node.outerHTML
+			)
+		);
+	} );
+}
+
 /**
  * Converts an HTML string to known blocks. Strips everything else.
  *
@@ -79,7 +124,7 @@ function getRawTransformations() {
  *
  * @return {Array|string} A list of blocks or a string, depending on `handlerMode`.
  */
-export default function rawHandler( { HTML = '', plainText = '', mode = 'AUTO', tagName, canUserUseUnfilteredHTML = false } ) {
+export function pasteHandler( { HTML = '', plainText = '', mode = 'AUTO', tagName, canUserUseUnfilteredHTML = false } ) {
 	// First of all, strip any meta tags.
 	HTML = HTML.replace( /<meta[^>]+>/, '' );
 
@@ -137,9 +182,9 @@ export default function rawHandler( { HTML = '', plainText = '', mode = 'AUTO',
 		return filterInlineHTML( HTML );
 	}
 
-	const rawTransformations = getRawTransformations();
+	const rawTransforms = getRawTransformations();
 	const phrasingContentSchema = getPhrasingContentSchema();
-	const blockContentSchema = getBlockContentSchema( rawTransformations );
+	const blockContentSchema = getBlockContentSchema( rawTransforms );
 
 	const blocks = compact( flatMap( pieces, ( piece ) => {
 		// Already a block from shortcode.
@@ -176,37 +221,7 @@ export default function rawHandler( { HTML = '', plainText = '', mode = 'AUTO',
 		// Allows us to ask for this information when we get a report.
 		console.log( 'Processed HTML piece:\n\n', piece );
 
-		const doc = document.implementation.createHTMLDocument( '' );
-
-		doc.body.innerHTML = piece;
-
-		return Array.from( doc.body.children ).map( ( node ) => {
-			const rawTransformation = findTransform( rawTransformations, ( { isMatch } ) => isMatch( node ) );
-
-			if ( ! rawTransformation ) {
-				console.warn(
-					'A block registered a raw transformation schema for `' + node.nodeName + '` but did not match it. ' +
-					'Make sure there is a `selector` or `isMatch` property that can match the schema.\n' +
-					'Sanitized HTML: `' + node.outerHTML + '`'
-				);
-
-				return;
-			}
-
-			const { transform, blockName } = rawTransformation;
-
-			if ( transform ) {
-				return transform( node );
-			}
-
-			return createBlock(
-				blockName,
-				getBlockAttributes(
-					getBlockType( blockName ),
-					node.outerHTML
-				)
-			);
-		} );
+		return htmlToBlocks( { html: piece, rawTransforms } );
 	} ) );
 
 	// If we're allowed to return inline content and there is only one block
@@ -225,3 +240,48 @@ export default function rawHandler( { HTML = '', plainText = '', mode = 'AUTO',
 
 	return blocks;
 }
+
+/**
+ * Converts an HTML string to known blocks.
+ *
+ * @param {string} $1.HTML The HTML to convert.
+ *
+ * @return {Array} A list of blocks.
+ */
+export function rawHandler( { HTML = '' } ) {
+	// If we detect block delimiters, parse entirely as blocks.
+	if ( HTML.indexOf( '<!-- wp:' ) !== -1 ) {
+		return parseWithGrammar( HTML );
+	}
+
+	// An array of HTML strings and block objects. The blocks replace matched
+	// shortcodes.
+	const pieces = shortcodeConverter( HTML );
+	const rawTransforms = getRawTransformations();
+	const blockContentSchema = getBlockContentSchema( rawTransforms );
+
+	return compact( flatMap( pieces, ( piece ) => {
+		// Already a block from shortcode.
+		if ( typeof piece !== 'string' ) {
+			return piece;
+		}
+
+		// These filters are essential for some blocks to be able to transform
+		// from raw HTML. These filters move around some content or add
+		// additional tags, they do not remove any content.
+		const filters = [
+			// Needed to create more and nextpage blocks.
+			specialCommentConverter,
+			// Needed to create media blocks.
+			figureContentReducer,
+			// Needed to create the quote block, which cannot handle text
+			// without wrapper paragraphs.
+			blockquoteNormaliser,
+		];
+
+		piece = deepFilterHTML( piece, filters, blockContentSchema );
+		piece = normaliseBlocks( piece );
+
+		return htmlToBlocks( { html: piece, rawTransforms } );
+	} ) );
+}
diff --git a/packages/editor/src/components/block-drop-zone/index.js b/packages/editor/src/components/block-drop-zone/index.js
index 885a54fe5a4d73..3af8b0cff3a6f7 100644
--- a/packages/editor/src/components/block-drop-zone/index.js
+++ b/packages/editor/src/components/block-drop-zone/index.js
@@ -11,7 +11,7 @@ import {
 	withFilters,
 } from '@wordpress/components';
 import {
-	rawHandler,
+	pasteHandler,
 	getBlockTransforms,
 	findTransform,
 } from '@wordpress/blocks';
@@ -70,7 +70,7 @@ class BlockDropZone extends Component {
 	}
 
 	onHTMLDrop( HTML, position ) {
-		const blocks = rawHandler( { HTML, mode: 'BLOCKS' } );
+		const blocks = pasteHandler( { HTML, mode: 'BLOCKS' } );
 
 		if ( blocks.length ) {
 			this.props.insertBlocks( blocks, this.getInsertIndex( position ) );
diff --git a/packages/editor/src/components/block-list/block-invalid-warning.js b/packages/editor/src/components/block-list/block-invalid-warning.js
index c08e993d91814e..27520ac4b79bd0 100644
--- a/packages/editor/src/components/block-list/block-invalid-warning.js
+++ b/packages/editor/src/components/block-list/block-invalid-warning.js
@@ -94,7 +94,6 @@ const blockToHTML = ( block ) => createBlock( 'core/html', {
 } );
 const blockToBlocks = ( block ) => rawHandler( {
 	HTML: block.originalContent,
-	mode: 'BLOCKS',
 } );
 
 export default withDispatch( ( dispatch, { block } ) => {
diff --git a/packages/editor/src/components/block-settings-menu/block-html-convert-button.js b/packages/editor/src/components/block-settings-menu/block-html-convert-button.js
index 6403e28bff12aa..2e49c011e6d7f2 100644
--- a/packages/editor/src/components/block-settings-menu/block-html-convert-button.js
+++ b/packages/editor/src/components/block-settings-menu/block-html-convert-button.js
@@ -12,22 +12,17 @@ import BlockConvertButton from './block-convert-button';
 
 export default compose(
 	withSelect( ( select, { clientId } ) => {
-		const { getBlock, canUserUseUnfilteredHTML } = select( 'core/editor' );
-		const block = getBlock( clientId );
+		const block = select( 'core/editor' ).getBlock( clientId );
+
 		return {
 			block,
-			canUserUseUnfilteredHTML: canUserUseUnfilteredHTML(),
 			shouldRender: ( block && block.name === 'core/html' ),
 		};
 	} ),
-	withDispatch( ( dispatch, { block, canUserUseUnfilteredHTML } ) => ( {
+	withDispatch( ( dispatch, { block } ) => ( {
 		onClick: () => dispatch( 'core/editor' ).replaceBlocks(
 			block.clientId,
-			rawHandler( {
-				HTML: getBlockContent( block ),
-				mode: 'BLOCKS',
-				canUserUseUnfilteredHTML,
-			} ),
+			rawHandler( { HTML: getBlockContent( block ) } ),
 		),
 	} ) ),
 )( BlockConvertButton );
diff --git a/packages/editor/src/components/block-settings-menu/block-unknown-convert-button.js b/packages/editor/src/components/block-settings-menu/block-unknown-convert-button.js
index c3e5bc0ffe0586..e2bc0d3f8e0b7a 100644
--- a/packages/editor/src/components/block-settings-menu/block-unknown-convert-button.js
+++ b/packages/editor/src/components/block-settings-menu/block-unknown-convert-button.js
@@ -12,22 +12,17 @@ import BlockConvertButton from './block-convert-button';
 
 export default compose(
 	withSelect( ( select, { clientId } ) => {
-		const { canUserUseUnfilteredHTML, getBlock } = select( 'core/editor' );
-		const block = getBlock( clientId );
+		const block = select( 'core/editor' ).getBlock( clientId );
+
 		return {
 			block,
-			canUserUseUnfilteredHTML: canUserUseUnfilteredHTML(),
 			shouldRender: ( block && block.name === getFreeformContentHandlerName() ),
 		};
 	} ),
-	withDispatch( ( dispatch, { block, canUserUseUnfilteredHTML } ) => ( {
+	withDispatch( ( dispatch, { block } ) => ( {
 		onClick: () => dispatch( 'core/editor' ).replaceBlocks(
 			block.clientId,
-			rawHandler( {
-				HTML: serialize( block ),
-				mode: 'BLOCKS',
-				canUserUseUnfilteredHTML,
-			} )
+			rawHandler( { HTML: serialize( block ) } )
 		),
 	} ) ),
 )( BlockConvertButton );
diff --git a/packages/editor/src/components/rich-text/index.js b/packages/editor/src/components/rich-text/index.js
index 26e3b97a2b93b0..b048c442f594ed 100644
--- a/packages/editor/src/components/rich-text/index.js
+++ b/packages/editor/src/components/rich-text/index.js
@@ -23,7 +23,7 @@ import {
 import { createBlobURL } from '@wordpress/blob';
 import { BACKSPACE, DELETE, ENTER, rawShortcut } from '@wordpress/keycodes';
 import { withDispatch, withSelect } from '@wordpress/data';
-import { rawHandler, children, getBlockTransforms, findTransform } from '@wordpress/blocks';
+import { pasteHandler, children, getBlockTransforms, findTransform } from '@wordpress/blocks';
 import { withInstanceId, withSafeTimeout, compose } from '@wordpress/compose';
 import { isURL } from '@wordpress/url';
 import {
@@ -306,7 +306,7 @@ export class RichText extends Component {
 		// Note: a pasted file may have the URL as plain text.
 		if ( item && ! html ) {
 			const file = item.getAsFile ? item.getAsFile() : item;
-			const content = rawHandler( {
+			const content = pasteHandler( {
 				HTML: `<img src="${ createBlobURL( file ) }">`,
 				mode: 'BLOCKS',
 				tagName: this.props.tagName,
@@ -358,7 +358,7 @@ export class RichText extends Component {
 			mode = 'AUTO';
 		}
 
-		const content = rawHandler( {
+		const content = pasteHandler( {
 			HTML: html,
 			plainText,
 			mode,
diff --git a/test/integration/__snapshots__/blocks-raw-handling.spec.js.snap b/test/integration/__snapshots__/blocks-raw-handling.spec.js.snap
new file mode 100644
index 00000000000000..84028b7c5f539b
--- /dev/null
+++ b/test/integration/__snapshots__/blocks-raw-handling.spec.js.snap
@@ -0,0 +1,35 @@
+// Jest Snapshot v1, https://goo.gl/fbAQLP
+
+exports[`Blocks raw handling rawHandler should convert HTML post to blocks with minimal content changes 1`] = `
+"<!-- wp:heading -->
+<h2>Howdy</h2>
+<!-- /wp:heading -->
+
+<!-- wp:image -->
+<figure class=\\"wp-block-image\\"><img src=\\"https://w.org\\" alt=\\"\\"/></figure>
+<!-- /wp:image -->
+
+<!-- wp:paragraph -->
+<p>This is a paragraph.</p>
+<!-- /wp:paragraph -->
+
+<!-- wp:paragraph -->
+<p>Preserve <span style=\\"color:red\\">me</span>!</p>
+<!-- /wp:paragraph -->
+
+<!-- wp:heading {\\"level\\":3} -->
+<h3>More tag</h3>
+<!-- /wp:heading -->
+
+<!-- wp:more -->
+<!--more-->
+<!-- /wp:more -->
+
+<!-- wp:heading {\\"level\\":3} -->
+<h3>Shortcode</h3>
+<!-- /wp:heading -->
+
+<!-- wp:gallery {\\"columns\\":3,\\"linkTo\\":\\"attachment\\"} -->
+<ul class=\\"wp-block-gallery columns-3 is-cropped\\"><li class=\\"blocks-gallery-item\\"><figure><img data-id=\\"1\\" class=\\"wp-image-1\\"/></figure></li></ul>
+<!-- /wp:gallery -->"
+`;
diff --git a/test/integration/blocks-raw-handling.spec.js b/test/integration/blocks-raw-handling.spec.js
index 26bee315fc5a51..b0997d3b757d9a 100644
--- a/test/integration/blocks-raw-handling.spec.js
+++ b/test/integration/blocks-raw-handling.spec.js
@@ -9,11 +9,16 @@ import path from 'path';
  */
 import {
 	getBlockContent,
+	pasteHandler,
 	rawHandler,
 	serialize,
 } from '@wordpress/blocks';
 import { registerCoreBlocks } from '@wordpress/block-library';
 
+function readFile( filePath ) {
+	return fs.existsSync( filePath ) ? fs.readFileSync( filePath, 'utf8' ).trim() : '';
+}
+
 describe( 'Blocks raw handling', () => {
 	beforeAll( () => {
 		// Load all hooks that modify blocks
@@ -22,7 +27,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should filter inline content', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: '<h2><em>test</em></h2>',
 			mode: 'INLINE',
 		} );
@@ -32,7 +37,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should parse Markdown', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: '* one<br>* two<br>* three',
 			plainText: '* one\n* two\n* three',
 			mode: 'AUTO',
@@ -43,7 +48,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should parse inline Markdown', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: 'Some **bold** text.',
 			plainText: 'Some **bold** text.',
 			mode: 'AUTO',
@@ -54,7 +59,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should parse HTML in plainText', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: '&lt;p&gt;Some &lt;strong&gt;bold&lt;/strong&gt; text.&lt;/p&gt;',
 			plainText: '<p>Some <strong>bold</strong> text.</p>',
 			mode: 'AUTO',
@@ -65,7 +70,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should parse Markdown with HTML', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: '',
 			plainText: '# Some <em>heading</em>\n\nA paragraph.',
 			mode: 'AUTO',
@@ -76,7 +81,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should break up forced inline content', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: '<p>test</p><p>test</p>',
 			mode: 'INLINE',
 		} );
@@ -86,7 +91,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should normalize decomposed characters', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: 'schön',
 			mode: 'INLINE',
 		} );
@@ -96,7 +101,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should treat single list item as inline text', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: '<ul><li>Some <strong>bold</strong> text.</li></ul>',
 			plainText: 'Some <strong>bold</strong> text.\n',
 			mode: 'AUTO',
@@ -107,7 +112,7 @@ describe( 'Blocks raw handling', () => {
 	} );
 
 	it( 'should treat multiple list items as a block', () => {
-		const filtered = rawHandler( {
+		const filtered = pasteHandler( {
 			HTML: '<ul><li>One</li><li>Two</li><li>Three</li></ul>',
 			plainText: 'One\nTwo\nThree\n',
 			mode: 'AUTO',
@@ -117,11 +122,7 @@ describe( 'Blocks raw handling', () => {
 		expect( console ).toHaveLogged();
 	} );
 
-	describe( 'serialize', () => {
-		function readFile( filePath ) {
-			return fs.existsSync( filePath ) ? fs.readFileSync( filePath, 'utf8' ).trim() : '';
-		}
-
+	describe( 'pasteHandler', () => {
 		[
 			'plain',
 			'classic',
@@ -143,7 +144,7 @@ describe( 'Blocks raw handling', () => {
 				const HTML = readFile( path.join( __dirname, `fixtures/${ type }-in.html` ) );
 				const plainText = readFile( path.join( __dirname, `fixtures/${ type }-in.txt` ) );
 				const output = readFile( path.join( __dirname, `fixtures/${ type }-out.html` ) );
-				const converted = rawHandler( { HTML, plainText, canUserUseUnfilteredHTML: true } );
+				const converted = pasteHandler( { HTML, plainText, canUserUseUnfilteredHTML: true } );
 				const serialized = typeof converted === 'string' ? converted : serialize( converted );
 
 				expect( serialized ).toBe( output );
@@ -154,4 +155,11 @@ describe( 'Blocks raw handling', () => {
 			} );
 		} );
 	} );
+
+	describe( 'rawHandler', () => {
+		it( 'should convert HTML post to blocks with minimal content changes', () => {
+			const HTML = readFile( path.join( __dirname, 'fixtures/wordpress-convert.html' ) );
+			expect( serialize( rawHandler( { HTML } ) ) ).toMatchSnapshot();
+		} );
+	} );
 } );
diff --git a/test/integration/fixtures/wordpress-convert.html b/test/integration/fixtures/wordpress-convert.html
new file mode 100644
index 00000000000000..1cb01568c37059
--- /dev/null
+++ b/test/integration/fixtures/wordpress-convert.html
@@ -0,0 +1,8 @@
+<h2>Howdy</h2>
+<img src="https://w.org">
+<p>This is a paragraph.</p>
+<p>Preserve <span style="color:red">me</span>!</p>
+<h3>More tag</h3>
+<p><!--more--></p>
+<h3>Shortcode</h3>
+<p>[gallery ids="1"]</p>