diff --git a/src/prompt_toolkit/formatted_text/ansi.py b/src/prompt_toolkit/formatted_text/ansi.py
index 2f355c2b7..9904f872c 100644
--- a/src/prompt_toolkit/formatted_text/ansi.py
+++ b/src/prompt_toolkit/formatted_text/ansi.py
@@ -291,7 +291,16 @@ def ansi_escape(text: object) -> str:
     """
     Replace characters with a special meaning.
     """
-    return str(text).replace("\x1b", "?").replace("\b", "?")
+    # Besides ESC, the parser also treats \x9b as the start of a control
+    # sequence, and everything between \001 and \002 as raw output.
+    return (
+        str(text)
+        .replace("\x1b", "?")
+        .replace("\x9b", "?")
+        .replace("\x01", "?")
+        .replace("\x02", "?")
+        .replace("\b", "?")
+    )
 
 
 class ANSIFormatter(Formatter):
diff --git a/src/prompt_toolkit/formatted_text/html.py b/src/prompt_toolkit/formatted_text/html.py
index a940ac8f8..94ea013a6 100644
--- a/src/prompt_toolkit/formatted_text/html.py
+++ b/src/prompt_toolkit/formatted_text/html.py
@@ -139,6 +139,7 @@ def html_escape(text: object) -> str:
         .replace("<", "&lt;")
         .replace(">", "&gt;")
         .replace('"', "&quot;")
+        .replace("'", "&#x27;")
     )
 
 
diff --git a/tests/test_formatted_text.py b/tests/test_formatted_text.py
index a111a7f20..484389713 100644
--- a/tests/test_formatted_text.py
+++ b/tests/test_formatted_text.py
@@ -209,6 +209,26 @@ def test_ansi_interpolation():
         ("ansigreen bg:ansimagenta", "2"),
     ]
 
+    # 8-bit CSI (\x9b) and the \001..\002 raw escape markers can't be
+    # injected through interpolated values either.
+    value = ANSI("{}").format("\x9b31mhi")
+    assert to_formatted_text(value) == [
+        ("", "?"),
+        ("", "3"),
+        ("", "1"),
+        ("", "m"),
+        ("", "h"),
+        ("", "i"),
+    ]
+
+    value = ANSI("%s") % "\x01x\x02y"
+    assert to_formatted_text(value) == [
+        ("", "?"),
+        ("", "x"),
+        ("", "?"),
+        ("", "y"),
+    ]
+
 
 def test_interpolation():
     value = Template(" {} ").format(HTML("<b>hello</b>"))
@@ -251,6 +271,13 @@ def test_html_interpolation():
     value = HTML("<b>{:02d}</b><u>{:.3f}</u>").format(3, 3.14159)
     assert to_formatted_text(value) == [("class:b", "03"), ("class:u", "3.142")]
 
+    # Quotes inside attribute values.
+    value = HTML("<style fg='{}'>x</style>").format("a'bg='b")
+    assert to_formatted_text(value) == [("fg:a'bg='b", "x")]
+
+    value = HTML('<style fg="%s">x</style>') % 'a"bg="b'
+    assert to_formatted_text(value) == [('fg:a"bg="b', "x")]
+
 
 def test_merge_formatted_text():
     html1 = HTML("<u>hello</u>")