diff --git a/src/MdToHTML.hs b/src/MdToHTML.hs
index 0e05836..dd863f8 100644
--- a/src/MdToHTML.hs
+++ b/src/MdToHTML.hs
@@ -120,6 +120,16 @@ fallthroughParser :: [ReadP a] -> ReadP a
 fallthroughParser [x] = x
 fallthroughParser (x : xs) = x <++ fallthroughParser xs
 
+myMany :: (Monoid a) => ReadP a -> ReadP [a]
+myMany p = do
+  remaining <- look
+  case remaining of
+    [] -> return []
+    _ -> return [] +++ myMany1 p
+
+myMany1 :: (Monoid a) => ReadP a -> ReadP [a]
+myMany1 p = liftM2 (:) p (myMany p)
+
 -- ---------------
 
 -- Parse a markdown header, denoted by 1-6 #'s followed by some text, followed by EOL.
@@ -143,19 +153,25 @@ parseBold = parseBoldWith "**" <|> parseBoldWith "__"
   where
     parseBoldWith delim = do
       string delim
-      inside <- many1 parseLineToken
+      inside <- myMany1 parseLineToken
       string delim
       return (Bold (Line inside))
 
 -- Parse italic text
 parseItalic :: ReadP MdToken
-parseItalic = parseItalicWith "*" <|> parseItalicWith "_"
+parseItalic = parseItalicWith '*' <|> parseItalicWith '_'
   where
     parseItalicWith delim = do
-      string delim
-      inside <- many1 parseLineToken
-      string delim
+      exactlyOnce delim
+      inside <- myMany1 parseLineToken
+      exactlyOnce delim
       return (Italic (Line inside))
+    exactlyOnce ch = do
+      char ch
+      remaining <- look
+      case remaining of
+        [] -> return ch
+        x : xs -> if x == ch then pfail else return ch
 
 -- Parse strikethrough text
 parseStrikethrough :: ReadP MdToken
@@ -250,7 +266,7 @@ parseLine :: ReadP MdToken
 parseLine = do
   skipSpaces
   -- Fail if we have reached the end of the document.
-  parsed <- manyTill parseLineToken eof
+  parsed <- myMany1 parseLineToken
   return (Line parsed)
 
 -- Parse a paragraph, which is a 'Line' (can span multiple actual lines), separated by double-newlines.
diff --git a/src/MdToHtmlTest.hs b/src/MdToHtmlTest.hs
index f36c6d8..9885853 100644
--- a/src/MdToHtmlTest.hs
+++ b/src/MdToHtmlTest.hs
@@ -22,6 +22,7 @@ headerTests =
 boldTests =
   TestList
     [ check_equal "Should convert bold" "<p><b>Hello</b></p>" (convert "__Hello__"),
+      check_equal " Should not convert incomplete bold" "<p>**Hello</p>" (convert "**Hello"),
       check_equal "Should convert italic" "<p><i>Hello</i></p>" (convert "_Hello_"),
       check_equal "Should convert bold and italic in a sentence" "<p>It <i>is</i> a <b>wonderful</b> day</p>" (convert "It _is_ a __wonderful__ day"),
       check_equal "Should convert nested bold and italic" "<p><b>Bold then <i>Italic</i></b></p>" (convert "**Bold then *Italic***"),