diff --git a/docs/qapi-code-gen.txt b/docs/qapi-code-gen.txt
index 3272b24..ff57010 100644
--- a/docs/qapi-code-gen.txt
+++ b/docs/qapi-code-gen.txt
@@ -182,11 +182,11 @@ prevent incomplete include files.

 Usage: { 'struct': STRING, 'data': DICT, '*base': STRUCT-NAME }

-A struct is a dictionary containing a single 'data' key whose
-value is a dictionary.  This corresponds to a struct in C or an Object
-in JSON. Each value of the 'data' dictionary must be the name of a
-type, or a one-element array containing a type name.  An example of a
-struct is:
+A struct is a dictionary containing a single 'data' key whose value is
+a dictionary; the dictionary may be empty.  This corresponds to a
+struct in C or an Object in JSON. Each value of the 'data' dictionary
+must be the name of a type, or a one-element array containing a type
+name.  An example of a struct is:

  { 'struct': 'MyType',
    'data': { 'member1': 'str', 'member2': 'int', '*member3': 'str' } }
@@ -277,7 +277,8 @@ Union types are used to let the user choose between several different
 variants for an object.  There are two flavors: simple (no
 discriminator or base), flat (both discriminator and base).  A union
 type is defined using a data dictionary as explained in the following
-paragraphs.
+paragraphs.  The data dictionary for either type of union must not
+be empty.

 A simple union type defines a mapping from automatic discriminator
 values to data types like in this example:
diff --git a/scripts/qapi.py b/scripts/qapi.py
index a0eca74..475d2c2 100644
--- a/scripts/qapi.py
+++ b/scripts/qapi.py
@@ -563,7 +563,10 @@ def check_union(expr, expr_info):
                                 "Discriminator '%s' must be of enumeration "
                                 "type" % discriminator)

-    # Check every branch
+    # Check every branch; don't allow an empty union
+    if len(members) == 0:
+        raise QAPIExprError(expr_info,
+                            "Union '%s' cannot have empty 'data'" % name)
     for (key, value) in members.items():
         check_name(expr_info, "Member of union '%s'" % name, key)

@@ -601,7 +604,11 @@ def check_alternate(expr, expr_info):
     values = { 'MAX': '(automatic)' }
     types_seen = {}

-    # Check every branch
+    # Check every branch; require at least two branches
+    if len(members) < 2:
+        raise QAPIExprError(expr_info,
+                            "Alternate '%s' should have at least two branches "
+                            "in 'data'" % name)
     for (key, value) in members.items():
         check_name(expr_info, "Member of alternate '%s'" % name, key)

@@ -964,6 +971,7 @@ class QAPISchemaObjectTypeVariants(object):
     def __init__(self, tag_name, tag_enum, variants):
         assert tag_name is None or isinstance(tag_name, str)
         assert tag_enum is None or isinstance(tag_enum, str)
+        assert len(variants) > 0
         for v in variants:
             assert isinstance(v, QAPISchemaObjectTypeVariant)
         self._tag_name = tag_name
diff --git a/tests/qapi-schema/alternate-empty.err b/tests/qapi-schema/alternate-empty.err
index e69de29..bb06c5b 100644
--- a/tests/qapi-schema/alternate-empty.err
+++ b/tests/qapi-schema/alternate-empty.err
@@ -0,0 +1 @@
+tests/qapi-schema/alternate-empty.json:2: Alternate 'Alt' should have at least two branches in 'data'
diff --git a/tests/qapi-schema/alternate-empty.exit b/tests/qapi-schema/alternate-empty.exit
index 573541a..d00491f 100644
--- a/tests/qapi-schema/alternate-empty.exit
+++ b/tests/qapi-schema/alternate-empty.exit
@@ -1 +1 @@
-0
+1
diff --git a/tests/qapi-schema/alternate-empty.json b/tests/qapi-schema/alternate-empty.json
index db3820f..fff15ba 100644
--- a/tests/qapi-schema/alternate-empty.json
+++ b/tests/qapi-schema/alternate-empty.json
@@ -1,2 +1,2 @@
-# FIXME - alternates should list at least two types to be useful
+# alternates must list at least two types to be useful
 { 'alternate': 'Alt', 'data': { 'i': 'int' } }
diff --git a/tests/qapi-schema/alternate-empty.out b/tests/qapi-schema/alternate-empty.out
index 9b010d8..e69de29 100644
--- a/tests/qapi-schema/alternate-empty.out
+++ b/tests/qapi-schema/alternate-empty.out
@@ -1,3 +0,0 @@
-object :empty
-alternate Alt
-    case i: int
diff --git a/tests/qapi-schema/flat-union-empty.err b/tests/qapi-schema/flat-union-empty.err
index e69de29..15754f5 100644
--- a/tests/qapi-schema/flat-union-empty.err
+++ b/tests/qapi-schema/flat-union-empty.err
@@ -0,0 +1 @@
+tests/qapi-schema/flat-union-empty.json:4: Union 'Union' cannot have empty 'data'
diff --git a/tests/qapi-schema/flat-union-empty.exit b/tests/qapi-schema/flat-union-empty.exit
index 573541a..d00491f 100644
--- a/tests/qapi-schema/flat-union-empty.exit
+++ b/tests/qapi-schema/flat-union-empty.exit
@@ -1 +1 @@
-0
+1
diff --git a/tests/qapi-schema/flat-union-empty.json b/tests/qapi-schema/flat-union-empty.json
index 67dd297..77f1d9a 100644
--- a/tests/qapi-schema/flat-union-empty.json
+++ b/tests/qapi-schema/flat-union-empty.json
@@ -1,4 +1,4 @@
-# FIXME - flat unions should not be empty
+# flat unions cannot be empty
 { 'enum': 'Empty', 'data': [ ] }
 { 'struct': 'Base', 'data': { 'type': 'Empty' } }
 { 'union': 'Union', 'base': 'Base', 'discriminator': 'type', 'data': { } }
diff --git a/tests/qapi-schema/flat-union-empty.out b/tests/qapi-schema/flat-union-empty.out
index 0e0665a..e69de29 100644
--- a/tests/qapi-schema/flat-union-empty.out
+++ b/tests/qapi-schema/flat-union-empty.out
@@ -1,7 +0,0 @@
-object :empty
-object Base
-    member type: Empty optional=False
-enum Empty []
-object Union
-    base Base
-    tag type
diff --git a/tests/qapi-schema/union-empty.err b/tests/qapi-schema/union-empty.err
index e69de29..12c2022 100644
--- a/tests/qapi-schema/union-empty.err
+++ b/tests/qapi-schema/union-empty.err
@@ -0,0 +1 @@
+tests/qapi-schema/union-empty.json:2: Union 'Union' cannot have empty 'data'
diff --git a/tests/qapi-schema/union-empty.exit b/tests/qapi-schema/union-empty.exit
index 573541a..d00491f 100644
--- a/tests/qapi-schema/union-empty.exit
+++ b/tests/qapi-schema/union-empty.exit
@@ -1 +1 @@
-0
+1
diff --git a/tests/qapi-schema/union-empty.json b/tests/qapi-schema/union-empty.json
index 1785007..1f0b13c 100644
--- a/tests/qapi-schema/union-empty.json
+++ b/tests/qapi-schema/union-empty.json
@@ -1,2 +1,2 @@
-# FIXME - unions should not be empty
+# unions cannot be empty
 { 'union': 'Union', 'data': { } }
diff --git a/tests/qapi-schema/union-empty.out b/tests/qapi-schema/union-empty.out
index c5500da..e69de29 100644
--- a/tests/qapi-schema/union-empty.out
+++ b/tests/qapi-schema/union-empty.out
@@ -1,4 +0,0 @@
-object :empty
-object Union
-    tag type
-enum UnionKind []
