diff --git a/pandoc.cabal b/pandoc.cabal
index f8cc78c64..d84012183 100644
--- a/pandoc.cabal
+++ b/pandoc.cabal
@@ -247,10 +247,7 @@ Extra-Source-Files:
                  test/odt/odt/*.odt
                  test/odt/markdown/*.md
                  test/odt/native/*.native
-                 test/lua/hello-world-doc.lua
-                 test/lua/markdown-reader.lua
-                 test/lua/plain-to-para.lua
-                 test/lua/strmacro.lua
+                 test/lua/*.lua
 Source-repository head
   type:          git
   location:      git://github.com/jgm/pandoc.git
diff --git a/src/Text/Pandoc/Lua.hs b/src/Text/Pandoc/Lua.hs
index d8b9f62f0..a89da52bc 100644
--- a/src/Text/Pandoc/Lua.hs
+++ b/src/Text/Pandoc/Lua.hs
@@ -34,7 +34,7 @@ import Control.Monad ( (>=>), when )
 import Control.Monad.Trans ( MonadIO(..) )
 import Data.Map ( Map )
 import Scripting.Lua ( LuaState, StackValue(..) )
-import Text.Pandoc.Definition ( Block(..), Inline(..), Pandoc(..) )
+import Text.Pandoc.Definition
 import Text.Pandoc.Lua.PandocModule ( pushPandocModule )
 import Text.Pandoc.Lua.StackInstances ()
 import Text.Pandoc.Walk
@@ -135,6 +135,12 @@ execInlineLuaFilter lua fnMap x = do
         case Map.lookup fnName fnMap of
           Nothing -> return x
           Just fn -> callFilterFn fn
+  let tryFilterAlternatives :: [(String, LuaFilterFunction Inline -> IO Inline)] -> IO Inline
+      tryFilterAlternatives [] = return x
+      tryFilterAlternatives ((fnName, callFilterFn) : alternatives) =
+        case Map.lookup fnName fnMap of
+          Nothing -> tryFilterAlternatives alternatives
+          Just fn -> callFilterFn fn
   case x of
     LineBreak                 -> tryFilter "LineBreak" runFn
     SoftBreak                 -> tryFilter "SoftBreak" runFn
@@ -142,9 +148,7 @@ execInlineLuaFilter lua fnMap x = do
     Cite cs lst               -> tryFilter "Cite"      $ \fn -> runFn fn lst cs
     Code attr str             -> tryFilter "Code"      $ \fn -> runFn fn str attr
     Emph lst                  -> tryFilter "Emph"      $ \fn -> runFn fn lst
-    Math mt lst               -> tryFilter "Math"      $ \fn -> runFn fn lst mt
     Note blks                 -> tryFilter "Note"      $ \fn -> runFn fn blks
-    Quoted qt lst             -> tryFilter "Quoted"    $ \fn -> runFn fn qt lst
     RawInline f str           -> tryFilter "RawInline" $ \fn -> runFn fn f str
     SmallCaps lst             -> tryFilter "SmallCaps" $ \fn -> runFn fn lst
     Span attr lst             -> tryFilter "Span"      $ \fn -> runFn fn lst attr
@@ -153,6 +157,22 @@ execInlineLuaFilter lua fnMap x = do
     Strong lst                -> tryFilter "Strong"    $ \fn -> runFn fn lst
     Subscript lst             -> tryFilter "Subscript" $ \fn -> runFn fn lst
     Superscript lst           -> tryFilter "Superscript" $ \fn -> runFn fn lst
+    Math DisplayMath lst      -> tryFilterAlternatives
+                                 [ ("DisplayMath", \fn -> runFn fn lst)
+                                 , ("Math", \fn -> runFn fn DisplayMath lst)
+                                 ]
+    Math InlineMath lst       -> tryFilterAlternatives
+                                 [ ("InlineMath", \fn -> runFn fn lst)
+                                 , ("Math", \fn -> runFn fn InlineMath lst)
+                                 ]
+    Quoted SingleQuote lst    -> tryFilterAlternatives
+                                 [ ("SingleQuoted", \fn -> runFn fn lst)
+                                 , ("Quoted", \fn -> runFn fn SingleQuote lst)
+                                 ]
+    Quoted DoubleQuote lst    -> tryFilterAlternatives
+                                 [ ("DoubleQuoted", \fn -> runFn fn lst)
+                                 , ("Quoted", \fn -> runFn fn DoubleQuote lst)
+                                 ]
     Link attr txt (src, tit)  -> tryFilter "Link" $
                                  \fn -> runFn fn txt src tit attr
     Image attr alt (src, tit) -> tryFilter "Image" $
diff --git a/test/Tests/Lua.hs b/test/Tests/Lua.hs
index 4196ff4b7..80c733751 100644
--- a/test/Tests/Lua.hs
+++ b/test/Tests/Lua.hs
@@ -8,15 +8,28 @@ import Test.Tasty.HUnit (Assertion, assertEqual, testCase)
 import Test.Tasty.QuickCheck (ioProperty, testProperty)
 import Text.Pandoc.Arbitrary ()
 import Text.Pandoc.Definition (Block, Inline, Meta, Pandoc)
-import Text.Pandoc.Builder ( (<>), bulletList, doc, emph, linebreak, rawBlock
-                           , para, plain, space, str, strong)
+import Text.Pandoc.Builder ( (<>), bulletList, doc, doubleQuoted, emph
+                           , linebreak, rawBlock, singleQuoted, para, plain
+                           , space, str, strong)
 import Text.Pandoc.Lua
 
 import qualified Scripting.Lua as Lua
 
 tests :: [TestTree]
 tests =
-  [ testCase "macro expansion via filter" $
+  [ testProperty "inline elements can be round-tripped through the lua stack" $
+    \x -> ioProperty (roundtripEqual (x::Inline))
+
+  , testProperty "block elements can be round-tripped through the lua stack" $
+    \x -> ioProperty (roundtripEqual (x::Block))
+
+  , testProperty "meta blocks can be round-tripped through the lua stack" $
+    \x -> ioProperty (roundtripEqual (x::Meta))
+
+  , testProperty "documents can be round-tripped through the lua stack" $
+    \x -> ioProperty (roundtripEqual (x::Pandoc))
+
+  , testCase "macro expansion via filter" $
     assertFilterConversion "a '{{helloworld}}' string is expanded"
       "strmacro.lua"
       (doc . para $ str "{{helloworld}}")
@@ -40,17 +53,11 @@ tests =
       (doc $ rawBlock "markdown" "*charly* **delta**")
       (doc . para $ emph "charly" <> space <> strong "delta")
 
-  , testProperty "inline elements can be round-tripped through the lua stack" $
-    \x -> ioProperty (roundtripEqual (x::Inline))
-
-  , testProperty "block elements can be round-tripped through the lua stack" $
-    \x -> ioProperty (roundtripEqual (x::Block))
-
-  , testProperty "meta blocks can be round-tripped through the lua stack" $
-    \x -> ioProperty (roundtripEqual (x::Meta))
-
-  , testProperty "documents can be round-tripped through the lua stack" $
-    \x -> ioProperty (roundtripEqual (x::Pandoc))
+  , testCase "allow shorthand functions for quote types" $
+    assertFilterConversion "single quoted becomes double quoted string"
+      "single-to-double-quoted.lua"
+      (doc . para . singleQuoted $ str "simple")
+      (doc . para . doubleQuoted $ str "simple")
   ]
 
 assertFilterConversion :: String -> FilePath -> Pandoc -> Pandoc -> Assertion
diff --git a/test/lua/single-to-double-quoted.lua b/test/lua/single-to-double-quoted.lua
new file mode 100644
index 000000000..8a0a5732a
--- /dev/null
+++ b/test/lua/single-to-double-quoted.lua
@@ -0,0 +1,7 @@
+return {
+  {
+    SingleQuoted = function (content)
+      return pandoc.Quoted("DoubleQuote", content)
+    end,
+  }
+}