diff --git a/src/hb-ot-layout-private.hh b/src/hb-ot-layout-private.hh
index 9020c895a..1759520fd 100644
--- a/src/hb-ot-layout-private.hh
+++ b/src/hb-ot-layout-private.hh
@@ -237,23 +237,6 @@ enum {
   UPROPS_MASK_GEN_CAT   = 0x1Fu
 };
 
-enum space_t {
-  SPACE = 0,
-  SPACE_NBSP,
-  SPACE_EN,
-  SPACE_EM,
-  SPACE_EM_3,
-  SPACE_EM_4,
-  SPACE_EM_6,
-  SPACE_FIGURE,
-  SPACE_PUNCTUATION,
-  SPACE_THIN,
-  SPACE_HAIR,
-  SPACE_NARROW,
-  SPACE_MEDIUM,
-  SPACE_IDEOGRAPHIC,
-};
-
 static inline void
 _hb_glyph_info_set_unicode_props (hb_glyph_info_t *info, hb_unicode_funcs_t *unicode)
 {
@@ -331,36 +314,18 @@ _hb_glyph_info_is_unicode_space (const hb_glyph_info_t *info)
 	 HB_UNICODE_GENERAL_CATEGORY_SPACE_SEPARATOR;
 }
 static inline void
-_hb_glyph_info_set_unicode_space_for_char (hb_glyph_info_t *info, hb_codepoint_t u)
+_hb_glyph_info_set_unicode_space_fallback_type (hb_glyph_info_t *info, hb_unicode_funcs_t::space_t s)
 {
   if (unlikely (!_hb_glyph_info_is_unicode_space (info)))
     return;
-
-  space_t s;
-  switch (u)
-  {
-    default:      s = SPACE;		break; /* Shouldn't happen. */
-    case 0x00A0u: s = SPACE_NBSP;	break;
-    case 0x2002u: s = SPACE_EN;		break;
-    case 0x2003u: s = SPACE_EM;		break;
-    case 0x2004u: s = SPACE_EM_3;	break;
-    case 0x2005u: s = SPACE_EM_4;	break;
-    case 0x2006u: s = SPACE_EM_6;	break;
-    case 0x2007u: s = SPACE_FIGURE;	break;
-    case 0x2008u: s = SPACE_PUNCTUATION;break;
-    case 0x2009u: s = SPACE_THIN;	break;
-    case 0x200Au: s = SPACE_HAIR;	break;
-    case 0x202Fu: s = SPACE_NARROW;	break;
-    case 0x205Fu: s = SPACE_MEDIUM;	break;
-    case 0x3000u: s = SPACE_IDEOGRAPHIC;break;
-  }
-
   info->unicode_props() = (((unsigned int) s)<<8) | (info->unicode_props() & 0xFF);
 }
-static inline space_t
-_hb_glyph_info_get_unicode_space (const hb_glyph_info_t *info)
+static inline hb_unicode_funcs_t::space_t
+_hb_glyph_info_get_unicode_space_fallback_type (const hb_glyph_info_t *info)
 {
-  return _hb_glyph_info_is_unicode_space (info) ? (space_t) (info->unicode_props()>>8) : SPACE;
+  return _hb_glyph_info_is_unicode_space (info) ?
+	 (hb_unicode_funcs_t::space_t) (info->unicode_props()>>8) :
+	 hb_unicode_funcs_t::NOT_SPACE;
 }
 
 static inline bool _hb_glyph_info_ligated (const hb_glyph_info_t *info);
diff --git a/src/hb-ot-shape-normalize.cc b/src/hb-ot-shape-normalize.cc
index 0a4d40499..c86c634fb 100644
--- a/src/hb-ot-shape-normalize.cc
+++ b/src/hb-ot-shape-normalize.cc
@@ -98,7 +98,7 @@ static inline void
 output_char (hb_buffer_t *buffer, hb_codepoint_t unichar, hb_codepoint_t glyph)
 {
   buffer->cur().glyph_index() = glyph;
-  buffer->output_glyph (unichar);
+  buffer->output_glyph (unichar); /* This is very confusing indeed. */
   _hb_glyph_info_set_unicode_props (&buffer->prev(), buffer->unicode);
 }
 
@@ -164,7 +164,8 @@ decompose_current_character (const hb_ot_shape_normalize_context_t *c, bool shor
 {
   hb_buffer_t * const buffer = c->buffer;
   hb_codepoint_t u = buffer->cur().codepoint;
-  hb_codepoint_t glyph;
+  hb_codepoint_t glyph, space_glyph;
+  hb_unicode_funcs_t::space_t space_type;
 
   /* Kind of a cute waterfall here... */
   if (shortest && c->font->get_glyph (u, 0, &glyph))
@@ -173,6 +174,13 @@ decompose_current_character (const hb_ot_shape_normalize_context_t *c, bool shor
     skip_char (buffer);
   else if (!shortest && c->font->get_glyph (u, 0, &glyph))
     next_char (buffer, glyph);
+  else if (_hb_glyph_info_is_unicode_space (&buffer->cur()) &&
+	   (space_type = buffer->unicode->space_fallback_type (u)) != hb_unicode_funcs_t::NOT_SPACE &&
+	   c->font->get_glyph (0x0020u, 0, &space_glyph))
+  {
+    _hb_glyph_info_set_unicode_space_fallback_type (&buffer->cur(), space_type);
+    next_char (buffer, space_glyph);
+  }
   else
     next_char (buffer, glyph); /* glyph is initialized in earlier branches. */
 }
diff --git a/src/hb-unicode-private.hh b/src/hb-unicode-private.hh
index e729826bf..43bbed675 100644
--- a/src/hb-unicode-private.hh
+++ b/src/hb-unicode-private.hh
@@ -199,6 +199,46 @@ HB_UNICODE_FUNCS_IMPLEMENT_CALLBACKS_SIMPLE
     }
   }
 
+  enum space_t {
+    NOT_SPACE = 0,
+    SPACE_NBSP,
+    SPACE_EN,
+    SPACE_EM,
+    SPACE_EM_3,
+    SPACE_EM_4,
+    SPACE_EM_6,
+    SPACE_FIGURE,
+    SPACE_PUNCTUATION,
+    SPACE_THIN,
+    SPACE_HAIR,
+    SPACE_NARROW,
+    SPACE_MEDIUM,
+    SPACE_IDEOGRAPHIC,
+  };
+  static inline space_t
+  space_fallback_type (hb_codepoint_t u)
+  {
+    switch (u)
+    {
+      /* All GC=Zs chars that can use a fallback. */
+      default:	  return NOT_SPACE; /* Shouldn't happen. */
+      case 0x00A0u: return SPACE_NBSP;
+      case 0x2000u: return SPACE_EN;
+      case 0x2001u: return SPACE_EM;
+      case 0x2002u: return SPACE_EN;
+      case 0x2003u: return SPACE_EM;
+      case 0x2004u: return SPACE_EM_3;
+      case 0x2005u: return SPACE_EM_4;
+      case 0x2006u: return SPACE_EM_6;
+      case 0x2007u: return SPACE_FIGURE;
+      case 0x2008u: return SPACE_PUNCTUATION;
+      case 0x2009u: return SPACE_THIN;
+      case 0x200Au: return SPACE_HAIR;
+      case 0x202Fu: return SPACE_NARROW;
+      case 0x205Fu: return SPACE_MEDIUM;
+      case 0x3000u: return SPACE_IDEOGRAPHIC;
+    }
+  }
 
   struct {
 #define HB_UNICODE_FUNC_IMPLEMENT(name) hb_unicode_##name##_func_t name;
diff --git a/test/shaping/Makefile.am b/test/shaping/Makefile.am
index 5694572ab..607da6d04 100644
--- a/test/shaping/Makefile.am
+++ b/test/shaping/Makefile.am
@@ -52,6 +52,7 @@ TESTS = \
 	tests/indic-old-spec.tests \
 	tests/indic-pref-blocking.tests \
 	tests/mongolian-variation-selector.tests \
+	tests/spaces.tests \
 	tests/vertical.tests \
 	tests/zero-width-marks.tests \
 	$(NULL)
diff --git a/test/shaping/fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf b/test/shaping/fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf
new file mode 100644
index 000000000..213e7cedb
Binary files /dev/null and b/test/shaping/fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf differ
diff --git a/test/shaping/fonts/sha1sum/MANIFEST b/test/shaping/fonts/sha1sum/MANIFEST
index 785e6ef03..879d92971 100644
--- a/test/shaping/fonts/sha1sum/MANIFEST
+++ b/test/shaping/fonts/sha1sum/MANIFEST
@@ -2,6 +2,7 @@
 051d92f8bc6ff724511b296c27623f824de256e9.ttf
 191826b9643e3f124d865d617ae609db6a2ce203.ttf
 1a6f1687b7a221f9f2c834b0b360d3c8463b6daf.ttf
+1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf
 226bc2deab3846f1a682085f70c67d0421014144.ttf
 270b89df543a7e48e206a2d830c0e10e5265c630.ttf
 298c9e1d955f10f6f72c6915c3c6ff9bf9695cec.ttf
diff --git a/test/shaping/tests/MANIFEST b/test/shaping/tests/MANIFEST
index 6ae62dccb..457c2eb03 100644
--- a/test/shaping/tests/MANIFEST
+++ b/test/shaping/tests/MANIFEST
@@ -10,5 +10,6 @@ indic-joiner-candrabindu.tests
 indic-old-spec.tests
 indic-pref-blocking.tests
 mongolian-variation-selector.tests
+spaces.tests
 vertical.tests
 zero-width-marks.tests
diff --git a/test/shaping/tests/spaces.tests b/test/shaping/tests/spaces.tests
new file mode 100644
index 000000000..d9e5d09c5
--- /dev/null
+++ b/test/shaping/tests/spaces.tests
@@ -0,0 +1,17 @@
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+0020:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+00A0:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+1680:[gid0=0+692]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2000:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2001:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2002:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2003:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2004:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2005:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2006:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2007:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2008:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+2009:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+200A:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+202F:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+205F:[gid1=0+560]
+fonts/sha1sum/1c2c3fc37b2d4c3cb2ef726c6cdaaabd4b7f3eb9.ttf:--font-funcs=ot:U+3000:[gid1=0+560]