diff --git a/common/dict.c b/common/dict.c
index 62a7816..b7ab00d 100644
--- a/common/dict.c
+++ b/common/dict.c
@@ -122,7 +122,7 @@ lookup_or_create_bucket (p11_dict *dict,
 		return bucketp;
 
 	/* add a new entry for non-NULL val */
-	(*bucketp) = calloc (1, sizeof (dictbucket));
+	(*bucketp) = calloc (sizeof (dictbucket), 1);
 
 	if (*bucketp != NULL) {
 		(*bucketp)->key = (void*)key;
@@ -175,7 +175,7 @@ p11_dict_set (p11_dict *dict,
 		/* check that the collision rate isn't too high */
 		if (dict->num_items > dict->num_buckets) {
 			num_buckets = dict->num_buckets * 2 + 1;
-			new_buckets = (dictbucket **)calloc (num_buckets, sizeof (dictbucket *));
+			new_buckets = (dictbucket **)calloc (sizeof (dictbucket *), num_buckets);
 
 			/* Ignore failures, maybe we can expand later */
 			if(new_buckets) {
@@ -283,7 +283,7 @@ p11_dict_new (p11_dict_hasher hash_func,
 		dict->value_destroy_func = value_destroy_func;
 
 		dict->num_buckets = 9;
-		dict->buckets = (dictbucket **)calloc (dict->num_buckets, sizeof (dictbucket *));
+		dict->buckets = (dictbucket **)calloc (sizeof (dictbucket *), dict->num_buckets);
 		if (!dict->buckets) {
 			free (dict);
 			return NULL;
diff --git a/common/path.c b/common/path.c
index d0d1893..17a6230 100644
--- a/common/path.c
+++ b/common/path.c
@@ -94,21 +94,15 @@ p11_path_base (const char *path)
 }
 
 static inline bool
-is_path_separator (char ch)
+is_path_component_or_null (char ch)
 {
-	return (ch == '/'
+	return (ch == '\0' || ch == '/'
 #ifdef OS_WIN32
 			|| ch == '\\'
 #endif
 		);
 }
 
-static inline bool
-is_path_separator_or_null (char ch)
-{
-	return is_path_separator (ch) || ch == '\0';
-}
-
 static char *
 expand_homedir (const char *remainder)
 {
@@ -119,7 +113,7 @@ expand_homedir (const char *remainder)
 		return NULL;
 	}
 
-	while (is_path_separator (remainder[0]))
+	while (remainder[0] && is_path_component_or_null (remainder[0]))
 		remainder++;
 	if (remainder[0] == '\0')
 		remainder = NULL;
@@ -127,7 +121,7 @@ expand_homedir (const char *remainder)
 	/* Expand $XDG_CONFIG_HOME */
 	if (remainder != NULL &&
 	    strncmp (remainder, ".config", 7) == 0 &&
-	    is_path_separator_or_null (remainder[7])) {
+	    is_path_component_or_null (remainder[7])) {
 		env = getenv ("XDG_CONFIG_HOME");
 		if (env && env[0])
 			return p11_path_build (env, remainder + 8, NULL);
@@ -180,7 +174,7 @@ p11_path_expand (const char *path)
 	return_val_if_fail (path != NULL, NULL);
 
 	if (strncmp (path, "~", 1) == 0 &&
-	    is_path_separator_or_null (path[1])) {
+	    is_path_component_or_null (path[1])) {
 		return expand_homedir (path + 1);
 
 	} else {
@@ -241,27 +235,15 @@ p11_path_build (const char *path,
 	while (path != NULL) {
 		num = strlen (path);
 
-		/* Trim beginning of path */
-		while (is_path_separator (path[0])) {
-			/* But preserve the leading path component */
-			if (!at && !is_path_separator (path[1]))
-				break;
-			path++;
-			num--;
-		}
-
 		/* Trim end of the path */
 		until = (at > 0) ? 0 : 1;
-		while (num > until && is_path_separator_or_null (path[num - 1]))
+		while (num > until && is_path_component_or_null (path[num - 1]))
 			num--;
 
 		if (at != 0) {
-			if (num == 0) {
-				path = va_arg (va, const char *);
+			if (num == 0)
 				continue;
-			}
-			if (built[at - 1] != delim)
-				built[at++] = delim;
+			built[at++] = delim;
 		}
 
 		assert (at + num < len);
@@ -269,6 +251,10 @@ p11_path_build (const char *path,
 		at += num;
 
 		path = va_arg (va, const char *);
+
+		/* Trim beginning of path */
+		while (path && path[0] && is_path_component_or_null (path[0]))
+			path++;
 	}
 	va_end (va);
 
@@ -288,17 +274,17 @@ p11_path_parent (const char *path)
 
 	/* Find the end of the last component */
 	e = path + strlen (path);
-	while (e != path && is_path_separator_or_null (*e))
+	while (e != path && is_path_component_or_null (*e))
 		e--;
 
 	/* Find the beginning of the last component */
-	while (e != path && !is_path_separator_or_null (*e)) {
+	while (e != path && !is_path_component_or_null (*e)) {
 		had = true;
 		e--;
 	}
 
 	/* Find the end of the last component */
-	while (e != path && is_path_separator_or_null (*e))
+	while (e != path && is_path_component_or_null (*e))
 		e--;
 
 	if (e == path) {
@@ -327,7 +313,7 @@ p11_path_prefix (const char *string,
 
 	return a > b &&
 	       strncmp (string, prefix, b) == 0 &&
-	       is_path_separator_or_null (string[b]);
+	       is_path_component_or_null (string[b]);
 }
 
 void
diff --git a/common/test-path.c b/common/test-path.c
index cf4a8e3..2eb5444 100644
--- a/common/test-path.c
+++ b/common/test-path.c
@@ -88,49 +88,23 @@ static void
 test_build (void)
 {
 #ifdef OS_UNIX
-	assert_str_eq_free ("/",
-	                    p11_path_build ("/", NULL));
-	assert_str_eq_free ("/",
-	                    p11_path_build ("", "//", NULL));
-	assert_str_eq_free ("/root",
-	                    p11_path_build ("///root///", NULL));
-	assert_str_eq_free ("/root",
-	                    p11_path_build ("/", "root", NULL));
-	assert_str_eq_free ("/root",
-	                    p11_path_build ("", "/root", NULL));
-	assert_str_eq_free ("/root",
-	                    p11_path_build ("/root", "", NULL));
 	assert_str_eq_free ("/root/second",
 	                    p11_path_build ("/root", "second", NULL));
 	assert_str_eq_free ("/root/second",
 	                    p11_path_build ("/root", "/second", NULL));
 	assert_str_eq_free ("/root/second",
 	                    p11_path_build ("/root/", "second", NULL));
-	assert_str_eq_free ("/root/second",
-	                    p11_path_build ("/root//", "//second/", NULL));
-	assert_str_eq_free ("/root/second",
-	                    p11_path_build ("/root//", "", "//second/", NULL));
 	assert_str_eq_free ("/root/second/third",
 	                    p11_path_build ("/root", "second", "third", NULL));
 	assert_str_eq_free ("/root/second/third",
 	                    p11_path_build ("/root", "/second/third", NULL));
 #else /* OS_WIN32 */
-	assert_str_eq_free ("C:\\root",
-	                    p11_path_build ("C:\\", "root", NULL));
-	assert_str_eq_free ("C:\\root",
-	                    p11_path_build ("", "C:\\root", NULL));
-	assert_str_eq_free ("C:\\root",
-	                    p11_path_build ("C:\\root", "", NULL));
 	assert_str_eq_free ("C:\\root\\second",
 	                    p11_path_build ("C:\\root", "second", NULL));
 	assert_str_eq_free ("C:\\root\\second",
 	                    p11_path_build ("C:\\root", "\\second", NULL));
 	assert_str_eq_free ("C:\\root\\second",
 	                    p11_path_build ("C:\\root\\", "second", NULL));
-	assert_str_eq_free ("C:\\root\\second",
-	                    p11_path_build ("C:\\root\\\\", "\\\\second", NULL));
-	assert_str_eq_free ("C:\\root\\second",
-	                    p11_path_build ("C:\\root\\\\", "", "\\\\second", NULL));
 	assert_str_eq_free ("C:\\root\\second\\third",
 	                    p11_path_build ("C:\\root", "second", "third", NULL));
 	assert_str_eq_free ("C:\\root\\second/third",
diff --git a/p11-kit/proxy.c b/p11-kit/proxy.c
index df18ac0..97c9b09 100644
--- a/p11-kit/proxy.c
+++ b/p11-kit/proxy.c
@@ -265,7 +265,7 @@ proxy_list_slots (Proxy *py, Mapping *mappings, unsigned int n_mappings)
 		/* Ask module for its slots */
 		rv = (funcs->C_GetSlotList) (FALSE, NULL, &count);
 		if (rv == CKR_OK && count) {
-			slots = calloc (count, sizeof (CK_SLOT_ID));
+			slots = calloc (sizeof (CK_SLOT_ID), count);
 			rv = (funcs->C_GetSlotList) (FALSE, slots, &count);
 		}
 
@@ -744,7 +744,7 @@ proxy_C_CloseAllSessions (CK_X_FUNCTION_LIST *self,
                           CK_SLOT_ID id)
 {
 	State *state = (State *)self;
-	CK_SESSION_HANDLE_PTR to_close = NULL;
+	CK_SESSION_HANDLE_PTR to_close;
 	CK_RV rv = CKR_OK;
 	Session *sess;
 	CK_ULONG i, count = 0;
@@ -756,7 +756,7 @@ proxy_C_CloseAllSessions (CK_X_FUNCTION_LIST *self,
 			rv = CKR_CRYPTOKI_NOT_INITIALIZED;
 		} else {
 			assert (state->px->sessions != NULL);
-			to_close = calloc (p11_dict_size (state->px->sessions) + 1, sizeof (CK_SESSION_HANDLE));
+			to_close = calloc (sizeof (CK_SESSION_HANDLE), p11_dict_size (state->px->sessions));
 			if (!to_close) {
 				rv = CKR_HOST_MEMORY;
 			} else {
diff --git a/trust/anchor.c b/trust/anchor.c
index 5ba5065..fab9cf6 100644
--- a/trust/anchor.c
+++ b/trust/anchor.c
@@ -64,10 +64,9 @@ create_arg_file_parser (void)
 	return_val_if_fail (parser != NULL, NULL);
 
 	p11_parser_formats (parser,
-			    p11_parser_format_persist,
-			    p11_parser_format_x509,
-			    p11_parser_format_pem,
-			    NULL);
+	                    p11_parser_format_x509,
+	                    p11_parser_format_pem,
+	                    NULL);
 
 	return parser;
 }