diff --git a/src/MdToHTML.hs b/src/MdToHTML.hs
index 57c58c3..18cd2a9 100644
--- a/src/MdToHTML.hs
+++ b/src/MdToHTML.hs
@@ -166,32 +166,31 @@ parseHeader = do
 
 -- Parse bold text
 parseBold :: ReadP MdToken
-parseBold = do
-  text <-
-    choice
-      [ between (string "__") (string "__") (many1 (lookaheadParse (/= "__"))),
-        between (string "**") (string "**") (many1 (lookaheadParse (/= "**")))
-      ]
-  let parsedText = fst $ leftmostLongestParse parseLine text
-  return (Bold parsedText)
+parseBold = parseBoldWith "**" <|> parseBoldWith "__"
+  where
+    parseBoldWith delim = do
+      string delim
+      inside <- greedyParse1 parseLineToken
+      string delim
+      return (Bold (Line inside))
 
 -- Parse italic text
 parseItalic :: ReadP MdToken
-parseItalic = do
-  text <-
-    choice
-      [ between (string "_") (string "_") (munch1 (/= '_')),
-        between (string "*") (string "*") (munch1 (/= '*'))
-      ]
-  let parsedText = fst $ leftmostLongestParse parseLine text
-  return (Italic parsedText)
+parseItalic = parseBoldWith "*" <|> parseBoldWith "_"
+  where
+    parseBoldWith delim = do
+      string delim
+      inside <- greedyParse1 parseLineToken
+      string delim
+      return (Italic (Line inside))
 
 -- Parse strikethrough text
 parseStrikethrough :: ReadP MdToken
 parseStrikethrough = do
-  text <- between (string "~~") (string "~~") (many1 (lookaheadParse (/= "~~")))
-  let parsedText = fst $ leftmostLongestParse parseLine text
-  return (Strikethrough parsedText)
+  string "~~"
+  inside <- many1 parseLineToken
+  string "~~"
+  return (Strikethrough (Line inside))
 
 -- Parse a link
 parseLink :: ReadP MdToken