diff --git a/pkgs/markdown/lib/src/block_parser.dart b/pkgs/markdown/lib/src/block_parser.dart
index 6111f55..6e1cf9f 100644
--- a/pkgs/markdown/lib/src/block_parser.dart
+++ b/pkgs/markdown/lib/src/block_parser.dart
@@ -219,7 +219,14 @@
   bool canParse(BlockParser parser) {
     // Note: matches *next* line, not the current one. We're looking for the
     // underlining after this line.
-    return parser.matchesNext(_setextPattern);
+    return parser.matchesNext(_setextPattern) &&
+        // The current line must look like a paragraph.
+        !(parser.matches(_codePattern) ||
+            parser.matches(_headerPattern) ||
+            parser.matches(_blockquotePattern) ||
+            parser.matches(_hrPattern) ||
+            parser.matches(_ulPattern) ||
+            parser.matches(_olPattern));
   }
 
   Node parse(BlockParser parser) {
@@ -278,6 +285,36 @@
 
   const BlockquoteSyntax();
 
+  List<String> parseChildLines(BlockParser parser) {
+    // Grab all of the lines that form the blockquote, stripping off the ">".
+    var childLines = <String>[];
+
+    while (!parser.isDone) {
+      var match = pattern.firstMatch(parser.current);
+      if (match != null) {
+        childLines.add(match[1]);
+        parser.advance();
+        continue;
+      }
+
+      // A paragraph continuation is OK. This is content that cannot be parsed
+      // as any other syntax except Paragraph, and it doesn't match the bar in
+      // a Setext header.
+      if (parser.blockSyntaxes.firstWhere((s) => s.canParse(parser))
+          is ParagraphSyntax) {
+        var continuedLine = childLines.last + parser.current;
+        childLines
+          ..removeLast()
+          ..add(continuedLine);
+        parser.advance();
+      } else {
+        break;
+      }
+    }
+
+    return childLines;
+  }
+
   Node parse(BlockParser parser) {
     var childLines = parseChildLines(parser);
 
@@ -547,11 +584,15 @@
         // Done with the list.
         break;
       } else {
-        // Anything else is paragraph text or other stuff that can be in a list
-        // item. However, if the previous item is a blank line, this means we're
-        // done with the list and are starting a new top-level paragraph.
-        if ((childLines.length > 0) && (childLines.last == '')) break;
-        childLines.add(parser.current);
+        // If the previous item is a blank line, this means we're done with the
+        // list and are starting a new top-level paragraph.
+        if ((childLines.isNotEmpty) && (childLines.last == '')) break;
+
+        // Anything else is paragraph continuation text.
+        var continuedLine = childLines.last + parser.current;
+        childLines
+          ..removeLast()
+          ..add(continuedLine);
       }
       parser.advance();
     }
diff --git a/pkgs/markdown/test/original/block_quotes.unit b/pkgs/markdown/test/original/block_quotes.unit
index 26d8ed7..14107ef 100644
--- a/pkgs/markdown/test/original/block_quotes.unit
+++ b/pkgs/markdown/test/original/block_quotes.unit
@@ -25,3 +25,18 @@
 <p>two</p>
 <blockquote>
 <p>three</p></blockquote></blockquote></blockquote>
+>>> quote turns what might be an h1 into nothing
+> quote
+===
+
+<<<
+<blockquote>
+<p>quote===</p></blockquote>
+>>> quote turns what might be an h2 into an hr
+> quote
+---
+
+<<<
+<blockquote>
+<p>quote</p></blockquote>
+<hr />
diff --git a/pkgs/markdown/test/original/setext_headers.unit b/pkgs/markdown/test/original/setext_headers.unit
index 6e610cf..65038f0 100644
--- a/pkgs/markdown/test/original/setext_headers.unit
+++ b/pkgs/markdown/test/original/setext_headers.unit
@@ -20,27 +20,3 @@
 
 <<<
 <p>-</p>
->>> h1 turns preceding list into text
-- list
-===
-
-<<<
-<h1>- list</h1>
->>> h2 turns preceding list into text
-- list
-===
-
-<<<
-<h1>- list</h1>
->>> h1 turns preceding blockquote into text
-> quote
-===
-
-<<<
-<h1>> quote</h1>
->>> h2 turns preceding blockquote into text
-> quote
-===
-
-<<<
-<h1>> quote</h1>
diff --git a/pkgs/markdown/test/original/unordered_lists.unit b/pkgs/markdown/test/original/unordered_lists.unit
index db40868..4729287 100644
--- a/pkgs/markdown/test/original/unordered_lists.unit
+++ b/pkgs/markdown/test/original/unordered_lists.unit
@@ -80,3 +80,16 @@
 <ul><li>
 <p>one</p><ul><li>nested one</li><li>nested two</li></ul></li><li>
 <p>two</p></li></ul>
+>>> list item turns what might be an h1 into nothing
+- list
+===
+
+<<<
+<ul><li>list===</li></ul>
+>>> list item turns what might be an h2 into nothing
+- list
+---
+
+<<<
+<ul><li>list</li></ul>
+<hr />