diff --git a/include/psa/crypto.h b/include/psa/crypto.h
index d3b7522ab..7291c3e57 100644
--- a/include/psa/crypto.h
+++ b/include/psa/crypto.h
@@ -459,9 +459,12 @@ psa_status_t psa_open_key(psa_key_id_t id,
  * maintain the key handle until after the multipart operation has finished.
  *
  * \param handle        The key handle to close.
+ *                      If this is \c 0, do nothing and return \c PSA_SUCCESS.
  *
  * \retval #PSA_SUCCESS
+ *         \p handle was a valid handle or \c 0. It is now closed.
  * \retval #PSA_ERROR_INVALID_HANDLE
+ *         \p handle is not a valid handle nor \c 0.
  * \retval #PSA_ERROR_COMMUNICATION_FAILURE
  * \retval #PSA_ERROR_CORRUPTION_DETECTED
  * \retval #PSA_ERROR_BAD_STATE
@@ -579,13 +582,17 @@ psa_status_t psa_copy_key(psa_key_handle_t source_handle,
  * key will cause the multipart operation to fail.
  *
  * \param handle        Handle to the key to erase.
+ *                      If this is \c 0, do nothing and return \c PSA_SUCCESS.
  *
  * \retval #PSA_SUCCESS
- *         The key material has been erased.
+ *         \p handle was a valid handle and the key material that it
+ *         referred to has been erased.
+ *         Alternatively, \p handle is \c 0.
  * \retval #PSA_ERROR_NOT_PERMITTED
  *         The key cannot be erased because it is
  *         read-only, either due to a policy or due to physical restrictions.
  * \retval #PSA_ERROR_INVALID_HANDLE
+ *         \p handle is not a valid handle nor \c 0.
  * \retval #PSA_ERROR_COMMUNICATION_FAILURE
  *         There was an failure in communication with the cryptoprocessor.
  *         The key material may still be present in the cryptoprocessor.
diff --git a/library/psa_crypto.c b/library/psa_crypto.c
index e26a7ec01..42c2969bf 100644
--- a/library/psa_crypto.c
+++ b/library/psa_crypto.c
@@ -1013,6 +1013,9 @@ psa_status_t psa_destroy_key( psa_key_handle_t handle )
     psa_se_drv_table_entry_t *driver;
 #endif /* MBEDTLS_PSA_CRYPTO_SE_C */
 
+    if( handle == 0 )
+        return( PSA_SUCCESS );
+
     status = psa_get_key_slot( handle, &slot );
     if( status != PSA_SUCCESS )
         return( status );
diff --git a/library/psa_crypto_slot_management.c b/library/psa_crypto_slot_management.c
index 59be319ce..6cd6a1135 100644
--- a/library/psa_crypto_slot_management.c
+++ b/library/psa_crypto_slot_management.c
@@ -255,6 +255,9 @@ psa_status_t psa_close_key( psa_key_handle_t handle )
     psa_status_t status;
     psa_key_slot_t *slot;
 
+    if( handle == 0 )
+        return( PSA_SUCCESS );
+
     status = psa_get_key_slot( handle, &slot );
     if( status != PSA_SUCCESS )
         return( status );
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index 6efdc01d1..fdeb0f3f4 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -43,15 +43,6 @@ PSA import/export AES-256
 depends_on:MBEDTLS_AES_C
 import_export:"0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef":PSA_KEY_TYPE_AES:PSA_KEY_USAGE_EXPORT:PSA_ALG_CTR:256:0:PSA_SUCCESS:1
 
-PSA invalid handle (0)
-invalid_handle:0
-
-PSA invalid handle (smallest plausible handle)
-invalid_handle:1
-
-PSA invalid handle (largest plausible handle)
-invalid_handle:-1
-
 PSA import: bad usage flag
 import_with_policy:PSA_KEY_TYPE_RAW_DATA:0x40000000:0:PSA_ERROR_INVALID_ARGUMENT
 
diff --git a/tests/suites/test_suite_psa_crypto.function b/tests/suites/test_suite_psa_crypto.function
index 87529ac6c..40e9e57e6 100644
--- a/tests/suites/test_suite_psa_crypto.function
+++ b/tests/suites/test_suite_psa_crypto.function
@@ -1103,9 +1103,6 @@ static int test_operations_on_invalid_handle( psa_key_handle_t handle )
                                        buffer, sizeof( buffer ), &length ),
                 PSA_ERROR_INVALID_HANDLE );
 
-    TEST_EQUAL( psa_close_key( handle ), PSA_ERROR_INVALID_HANDLE );
-    TEST_EQUAL( psa_destroy_key( handle ), PSA_ERROR_INVALID_HANDLE );
-
     ok = 1;
 
 exit:
@@ -1535,17 +1532,6 @@ exit:
 }
 /* END_CASE */
 
-/* BEGIN_CASE */
-void invalid_handle( int handle )
-{
-    PSA_ASSERT( psa_crypto_init( ) );
-    test_operations_on_invalid_handle( handle );
-
-exit:
-    PSA_DONE( );
-}
-/* END_CASE */
-
 /* BEGIN_CASE */
 void import_export_public_key( data_t *data,
                                int type_arg,
diff --git a/tests/suites/test_suite_psa_crypto_slot_management.data b/tests/suites/test_suite_psa_crypto_slot_management.data
index 6fa872312..803917dbe 100644
--- a/tests/suites/test_suite_psa_crypto_slot_management.data
+++ b/tests/suites/test_suite_psa_crypto_slot_management.data
@@ -148,8 +148,17 @@ Copy persistent to same
 depends_on:MBEDTLS_PSA_CRYPTO_STORAGE_C
 copy_to_occupied:PSA_KEY_LIFETIME_PERSISTENT:1:PSA_KEY_USAGE_EXPORT | PSA_KEY_USAGE_COPY:PSA_ALG_CTR:PSA_KEY_TYPE_AES:"404142434445464748494a4b4c4d4e4f":PSA_KEY_LIFETIME_PERSISTENT:1:PSA_KEY_USAGE_EXPORT:PSA_ALG_CTR:PSA_KEY_TYPE_AES:"404142434445464748494a4b4c4d4e4f"
 
-Close/destroy invalid handle
-invalid_handle:
+invalid handle: 0
+invalid_handle:INVALID_HANDLE_0:PSA_SUCCESS:PSA_ERROR_INVALID_HANDLE
+
+invalid handle: never opened
+invalid_handle:INVALID_HANDLE_UNOPENED:PSA_ERROR_INVALID_HANDLE:PSA_ERROR_INVALID_HANDLE
+
+invalid handle: already closed
+invalid_handle:INVALID_HANDLE_CLOSED:PSA_ERROR_INVALID_HANDLE:PSA_ERROR_INVALID_HANDLE
+
+invalid handle: huge
+invalid_handle:INVALID_HANDLE_HUGE:PSA_ERROR_INVALID_HANDLE:PSA_ERROR_INVALID_HANDLE
 
 Open many transient handles
 many_transient_handles:42
diff --git a/tests/suites/test_suite_psa_crypto_slot_management.function b/tests/suites/test_suite_psa_crypto_slot_management.function
index 3b9eada83..4c824f7de 100644
--- a/tests/suites/test_suite_psa_crypto_slot_management.function
+++ b/tests/suites/test_suite_psa_crypto_slot_management.function
@@ -20,6 +20,14 @@ typedef enum
     CLOSE_AFTER,
 } reopen_policy_t;
 
+typedef enum
+{
+    INVALID_HANDLE_0,
+    INVALID_HANDLE_UNOPENED,
+    INVALID_HANDLE_CLOSED,
+    INVALID_HANDLE_HUGE,
+} invalid_handle_construction_t;
+
 /* All test functions that create persistent keys must call
  * `TEST_USES_KEY_ID( key_id )` before creating a persistent key with this
  * identifier, and must call psa_purge_key_storage() in their cleanup
@@ -625,9 +633,13 @@ exit:
 /* END_CASE */
 
 /* BEGIN_CASE */
-void invalid_handle( )
+void invalid_handle( int handle_construction,
+                     int close_status_arg, int usage_status_arg )
 {
-    psa_key_handle_t handle1 = 0;
+    psa_key_handle_t valid_handle = 0;
+    psa_key_handle_t invalid_handle = 0;
+    psa_status_t close_status = close_status_arg;
+    psa_status_t usage_status = usage_status_arg;
     psa_key_attributes_t attributes = PSA_KEY_ATTRIBUTES_INIT;
     uint8_t material[1] = "a";
 
@@ -639,23 +651,50 @@ void invalid_handle( )
     psa_set_key_algorithm( &attributes, 0 );
     PSA_ASSERT( psa_import_key( &attributes,
                                 material, sizeof( material ),
-                                &handle1 ) );
-    TEST_ASSERT( handle1 != 0 );
+                                &valid_handle ) );
+    TEST_ASSERT( valid_handle != 0 );
 
-    /* Attempt to close and destroy some invalid handles. */
-    TEST_EQUAL( psa_close_key( 0 ), PSA_ERROR_INVALID_HANDLE );
-    TEST_EQUAL( psa_close_key( handle1 - 1 ), PSA_ERROR_INVALID_HANDLE );
-    TEST_EQUAL( psa_close_key( handle1 + 1 ), PSA_ERROR_INVALID_HANDLE );
-    TEST_EQUAL( psa_destroy_key( 0 ), PSA_ERROR_INVALID_HANDLE );
-    TEST_EQUAL( psa_destroy_key( handle1 - 1 ), PSA_ERROR_INVALID_HANDLE );
-    TEST_EQUAL( psa_destroy_key( handle1 + 1 ), PSA_ERROR_INVALID_HANDLE );
+    /* Construct an invalid handle as specified in the test case data. */
+    switch( handle_construction )
+    {
+        case INVALID_HANDLE_0:
+            invalid_handle = 0;
+            break;
+        case INVALID_HANDLE_UNOPENED:
+            /* We can't easily construct a handle that's never been opened
+             * without knowing how the implementation constructs handle
+             * values. The current test code assumes that valid handles
+             * are in a range between 1 and some maximum. */
+            if( valid_handle == 1 )
+                invalid_handle = 2;
+            else
+                invalid_handle = valid_handle - 1;
+            break;
+        case INVALID_HANDLE_CLOSED:
+            PSA_ASSERT( psa_import_key( &attributes,
+                                        material, sizeof( material ),
+                                        &invalid_handle ) );
+            PSA_ASSERT( psa_destroy_key( invalid_handle ) );
+            break;
+        case INVALID_HANDLE_HUGE:
+            invalid_handle = (psa_key_handle_t) ( -1 );
+            break;
+        default:
+            TEST_ASSERT( ! "unknown handle construction" );
+    }
+
+    /* Attempt to use the invalid handle. */
+    TEST_EQUAL( psa_get_key_attributes( invalid_handle, &attributes ),
+                usage_status );
+    TEST_EQUAL( psa_close_key( invalid_handle ), close_status );
+    TEST_EQUAL( psa_destroy_key( invalid_handle ), close_status );
 
     /* After all this, check that the original handle is intact. */
-    PSA_ASSERT( psa_get_key_attributes( handle1, &attributes ) );
+    PSA_ASSERT( psa_get_key_attributes( valid_handle, &attributes ) );
     TEST_EQUAL( psa_get_key_type( &attributes ), PSA_KEY_TYPE_RAW_DATA );
     TEST_EQUAL( psa_get_key_bits( &attributes ),
                 PSA_BYTES_TO_BITS( sizeof( material ) ) );
-    PSA_ASSERT( psa_close_key( handle1 ) );
+    PSA_ASSERT( psa_close_key( valid_handle ) );
 
 exit:
     PSA_DONE( );