diff --git a/src/keymap-dump.c b/src/keymap-dump.c
index 6311813..695c3be 100644
--- a/src/keymap-dump.c
+++ b/src/keymap-dump.c
@@ -565,7 +565,7 @@ write_keysyms(struct xkb_keymap *keymap, struct buf *buf,
 #define OUT_BUF_LEN 128
     char out_buf[OUT_BUF_LEN];
 
-    for (level = 0; level < XkbKeyGroupWidth(keymap, key, group); level++) {
+    for (level = 0; level < XkbKeyGroupWidth(key, group); level++) {
         if (level != 0)
             write_buf(buf, ", ");
         num_syms = xkb_keymap_key_get_syms_by_level(keymap, key->keycode,
@@ -634,13 +634,12 @@ write_symbols(struct xkb_keymap *keymap, struct buf *buf)
             if (key->groups[group].explicit_type)
                 explicit_types = true;
 
-            if (group != 0 &&
-                XkbKeyType(keymap, key, group) != XkbKeyType(keymap, key, 0))
+            if (group != 0 && key->groups[group].type != key->groups[0].type)
                 multi_type = true;
         }
 
         if (explicit_types) {
-            struct xkb_key_type *type = XkbKeyType(keymap, key, 0);
+            const struct xkb_key_type *type;
             simple = false;
 
             if (multi_type) {
@@ -648,13 +647,14 @@ write_symbols(struct xkb_keymap *keymap, struct buf *buf)
                     if (!key->groups[group].explicit_type)
                         continue;
 
-                    type = XkbKeyType(keymap, key, group);
+                    type = key->groups[group].type;
                     write_buf(buf, "\n\t\t\ttype[group%u]= \"%s\",",
                               group + 1,
                               xkb_atom_text(keymap->ctx, type->name));
                 }
             }
             else {
+                type = key->groups[0].type;
                 write_buf(buf, "\n\t\t\ttype= \"%s\",",
                           xkb_atom_text(keymap->ctx, type->name));
             }
@@ -713,8 +713,7 @@ write_symbols(struct xkb_keymap *keymap, struct buf *buf)
                     write_buf(buf, ",\n\t\t\tactions[Group%u]= [ ",
                               group + 1);
                     for (level = 0;
-                         level < XkbKeyGroupWidth(keymap, key, group);
-                         level++) {
+                         level < XkbKeyGroupWidth(key, group); level++) {
                         if (level != 0)
                             write_buf(buf, ", ");
                         write_action(keymap, buf,
diff --git a/src/keymap.c b/src/keymap.c
index daf3ab2..77afda7 100644
--- a/src/keymap.c
+++ b/src/keymap.c
@@ -91,7 +91,7 @@ xkb_keymap_unref(struct xkb_keymap *keymap)
 
     darray_foreach(key, keymap->keys) {
         for (i = 0; i < key->num_groups; i++) {
-            for (j = 0; j < XkbKeyGroupWidth(keymap, key, i); j++)
+            for (j = 0; j < XkbKeyGroupWidth(key, i); j++)
                 if (key->groups[i].levels[j].num_syms > 1)
                     free(key->groups[i].levels[j].u.syms);
             free(key->groups[i].levels);
@@ -248,7 +248,7 @@ xkb_keymap_num_levels_for_key(struct xkb_keymap *keymap, xkb_keycode_t kc,
     if (!key)
         return 0;
 
-    return XkbKeyGroupWidth(keymap, key, layout);
+    return XkbKeyGroupWidth(key, layout);
 }
 
 /**
@@ -318,7 +318,7 @@ xkb_keymap_key_get_syms_by_level(struct xkb_keymap *keymap,
         goto err;
     if (layout >= key->num_groups)
         goto err;
-    if (level >= XkbKeyGroupWidth(keymap, key, layout))
+    if (level >= XkbKeyGroupWidth(key, layout))
         goto err;
 
     num_syms = XkbKeyNumSyms(key, layout, level);
diff --git a/src/keymap.h b/src/keymap.h
index 243a5cf..0829c39 100644
--- a/src/keymap.h
+++ b/src/keymap.h
@@ -331,7 +331,8 @@ struct xkb_level {
 
 struct xkb_group {
     bool explicit_type;
-    unsigned type_index;
+    /* Points to a type in keymap->types. */
+    const struct xkb_key_type *type;
     /* Use XkbKeyGroupWidth for the number of levels. */
     struct xkb_level *levels;
 };
@@ -406,18 +407,10 @@ XkbKey(struct xkb_keymap *keymap, xkb_keycode_t kc)
 #define xkb_foreach_key(iter, keymap) \
     darray_foreach(iter, keymap->keys)
 
-static inline struct xkb_key_type *
-XkbKeyType(struct xkb_keymap *keymap, const struct xkb_key *key,
-           xkb_layout_index_t layout)
-{
-    return &keymap->types[key->groups[layout].type_index];
-}
-
 static inline xkb_level_index_t
-XkbKeyGroupWidth(struct xkb_keymap *keymap, const struct xkb_key *key,
-                 xkb_layout_index_t layout)
+XkbKeyGroupWidth(const struct xkb_key *key, xkb_layout_index_t layout)
 {
-    return XkbKeyType(keymap, key, layout)->num_levels;
+    return key->groups[layout].type->num_levels;
 }
 
 static inline unsigned int
diff --git a/src/state.c b/src/state.c
index 22ca9e5..0210d38 100644
--- a/src/state.c
+++ b/src/state.c
@@ -105,15 +105,15 @@ struct xkb_state {
     struct xkb_keymap *keymap;
 };
 
-static struct xkb_kt_map_entry *
+static const struct xkb_kt_map_entry *
 get_entry_for_key_state(struct xkb_state *state, const struct xkb_key *key,
                         xkb_layout_index_t group)
 {
-    struct xkb_key_type *type;
+    const struct xkb_key_type *type;
     xkb_mod_mask_t active_mods;
     unsigned int i;
 
-    type = XkbKeyType(state->keymap, key, group);
+    type = key->groups[group].type;
     active_mods = xkb_state_serialize_mods(state, XKB_STATE_EFFECTIVE);
     active_mods &= type->mods.mask;
 
@@ -133,7 +133,7 @@ xkb_state_key_get_level(struct xkb_state *state, xkb_keycode_t kc,
                         xkb_layout_index_t layout)
 {
     const struct xkb_key *key = XkbKey(state->keymap, kc);
-    struct xkb_kt_map_entry *entry;
+    const struct xkb_kt_map_entry *entry;
 
     if (!key || layout >= key->num_groups)
         return XKB_LEVEL_INVALID;
@@ -1019,7 +1019,7 @@ xkb_state_led_name_is_active(struct xkb_state *state, const char *name)
 static xkb_mod_mask_t
 key_get_consumed(struct xkb_state *state, const struct xkb_key *key)
 {
-    struct xkb_kt_map_entry *entry;
+    const struct xkb_kt_map_entry *entry;
     xkb_layout_index_t group;
 
     group = xkb_state_key_get_layout(state, key->keycode);
diff --git a/src/xkbcomp/keymap.c b/src/xkbcomp/keymap.c
index 93690a2..e8db5fd 100644
--- a/src/xkbcomp/keymap.c
+++ b/src/xkbcomp/keymap.c
@@ -139,7 +139,7 @@ ApplyInterpsToKey(struct xkb_keymap *keymap, struct xkb_key *key)
         return true;
 
     for (group = 0; group < key->num_groups; group++) {
-        width = XkbKeyGroupWidth(keymap, key, group);
+        width = XkbKeyGroupWidth(key, group);
         for (level = 0; level < width; level++) {
             struct xkb_sym_interpret *interp;
 
@@ -220,7 +220,7 @@ UpdateDerivedKeymapFields(struct xkb_keymap *keymap)
     /* Update action modifiers. */
     xkb_foreach_key(key, keymap)
         for (i = 0; i < key->num_groups; i++)
-            for (j = 0; j < XkbKeyGroupWidth(keymap, key, i); j++)
+            for (j = 0; j < XkbKeyGroupWidth(key, i); j++)
                 UpdateActionMods(keymap, &key->groups[i].levels[j].action,
                                  key->modmap);
 
diff --git a/src/xkbcomp/symbols.c b/src/xkbcomp/symbols.c
index 889a915..13c0887 100644
--- a/src/xkbcomp/symbols.c
+++ b/src/xkbcomp/symbols.c
@@ -1308,7 +1308,7 @@ FindKeyForSymbol(struct xkb_keymap *keymap, xkb_keysym_t sym)
 
     xkb_foreach_key(key, keymap) {
         for (group = 0; group < key->num_groups; group++) {
-            for (level = 0; level < XkbKeyGroupWidth(keymap, key, group);
+            for (level = 0; level < XkbKeyGroupWidth(key, group);
                  level++) {
                 if (XkbKeyNumSyms(key, group, level) != 1 ||
                     (XkbKeySymEntry(key, group, level))[0] != sym)
@@ -1338,13 +1338,14 @@ FindKeyForSymbol(struct xkb_keymap *keymap, xkb_keysym_t sym)
 }
 
 static bool
-FindNamedType(struct xkb_keymap *keymap, xkb_atom_t name, unsigned *type_rtrn)
+FindNamedType(struct xkb_keymap *keymap, xkb_atom_t name,
+              const struct xkb_key_type **type_rtrn)
 {
     unsigned int i;
 
     for (i = 0; i < keymap->num_types; i++) {
         if (keymap->types[i].name == name) {
-            *type_rtrn = i;
+            *type_rtrn = &keymap->types[i];
             return true;
         }
     }
@@ -1472,7 +1473,6 @@ CopySymbolsDef(SymbolsInfo *info, KeyInfo *keyi)
 
     /* * Find and assign the groups' types in the keymap. */
     darray_enumerate(i, groupi, keyi->groups) {
-        struct xkb_key_type *type;
         struct xkb_group *group = &key->groups[i];
         bool autoType = false;
 
@@ -1492,10 +1492,11 @@ CopySymbolsDef(SymbolsInfo *info, KeyInfo *keyi)
         }
 
         /* Find the type in the keymap, if it was defined in xkb_types. */
-        if (FindNamedType(keymap, groupi->type, &group->type_index)) {
+        if (FindNamedType(keymap, groupi->type, &group->type)) {
             if (!autoType || darray_size(groupi->levels) > 2)
                 key->groups[i].explicit_type = true;
         }
+        /* Not found, use a default. */
         else {
             log_vrb(info->keymap->ctx, 3,
                     "Type \"%s\" is not defined; "
@@ -1506,26 +1507,26 @@ CopySymbolsDef(SymbolsInfo *info, KeyInfo *keyi)
              * Index 0 is guaranteed to contain something, usually
              * ONE_LEVEL or at least some default one-level type.
              */
-            group->type_index = 0;
+            group->type = &keymap->types[0];
         }
 
         /* Always have as many levels as the type specifies. */
-        type = &keymap->types[group->type_index];
-        if (type->num_levels < darray_size(groupi->levels)) {
+        if (group->type->num_levels < darray_size(groupi->levels)) {
             struct xkb_level *leveli;
 
             log_vrb(info->keymap->ctx, 1,
                     "Type \"%s\" has %d levels, but %s has %d levels; "
                     "Ignoring extra symbols\n",
-                    xkb_atom_text(keymap->ctx, type->name),
-                    type->num_levels,
+                    xkb_atom_text(keymap->ctx, group->type->name),
+                    group->type->num_levels,
                     LongKeyNameText(keyi->name),
                     (int) darray_size(groupi->levels));
 
-            darray_foreach_from(leveli, groupi->levels, type->num_levels)
+            darray_foreach_from(leveli, groupi->levels,
+                                group->type->num_levels)
                 ClearLevelInfo(leveli);
         }
-        darray_resize0(groupi->levels, type->num_levels);
+        darray_resize0(groupi->levels, group->type->num_levels);
     }
 
     /* Copy levels. */