diff --git a/hy/models/set.py b/hy/models/set.py
index 3a81aed..fda7b52 100644
--- a/hy/models/set.py
+++ b/hy/models/set.py
@@ -18,19 +18,16 @@
 # FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 # DEALINGS IN THE SOFTWARE.
 
+from hy.models import _wrappers, wrap_value
 from hy.models.list import HyList
-from functools import reduce
 
 
 class HySet(HyList):
     """
-    Hy set (actually a list that pretends to be a set)
+    Hy set (just a representation of a set)
     """
 
-    def __init__(self, items):
-        items = sorted(items)
-        items = list(reduce(lambda r, v: v in r and r or r+[v], items, []))
-        super(HySet, self).__init__(items)
-
     def __repr__(self):
         return "#{%s}" % (" ".join([repr(x) for x in self]))
+
+_wrappers[set] = lambda s: HySet(wrap_value(x) for x in s)
diff --git a/tests/lex/test_lex.py b/tests/lex/test_lex.py
index 4413a6b..81407cc 100644
--- a/tests/lex/test_lex.py
+++ b/tests/lex/test_lex.py
@@ -230,6 +230,16 @@ def test_sets():
         HyExpression([HySymbol("baz"), HySymbol("quux")])
     ])]
 
+    # Duplicate items in a literal set should be okay (and should
+    # be preserved).
+    objs = tokenize("#{1 2 1 1 2 1}")
+    assert objs == [HySet([HyInteger(n) for n in [1, 2, 1, 1, 2, 1]])]
+    assert len(objs[0]) == 6
+
+    # https://github.com/hylang/hy/issues/1120
+    objs = tokenize("#{a 1}")
+    assert objs == [HySet([HySymbol("a"), HyInteger(1)])]
+
 
 def test_nospace():
     """ Ensure we can tokenize without spaces if we have to """
diff --git a/tests/models/test_set.py b/tests/models/test_set.py
index ceea726..0462c2c 100644
--- a/tests/models/test_set.py
+++ b/tests/models/test_set.py
@@ -5,4 +5,4 @@ hyset = HySet([3, 1, 2, 2])
 
 
 def test_set():
-    assert hyset == [1, 2, 3]
+    assert hyset == [3, 1, 2, 2]
diff --git a/tests/native_tests/language.hy b/tests/native_tests/language.hy
index 0300ffb..54b3e61 100644
--- a/tests/native_tests/language.hy
+++ b/tests/native_tests/language.hy
@@ -47,6 +47,7 @@
 (defn test-sets []
   "NATIVE: test sets work right"
   (assert (= #{1 2 3 4} (| #{1 2} #{3 4})))
+  (assert (= (type #{1 2 3 4}) set))
   (assert (= #{} (set))))
 
 
diff --git a/tests/native_tests/native_macros.hy b/tests/native_tests/native_macros.hy
index eca4538..788e52b 100644
--- a/tests/native_tests/native_macros.hy
+++ b/tests/native_tests/native_macros.hy
@@ -39,6 +39,9 @@
 (defmacro a-dict [] {1 2})
 (assert (= (a-dict) {1 2}))
 
+(defmacro a-set [] #{1 2})
+(assert (= (a-set) #{1 2}))
+
 (defmacro a-none [])
 (assert (= (a-none) None))