diff --git a/tests/suites/test_suite_asn1parse.data b/tests/suites/test_suite_asn1parse.data
index e917241..10333d3 100644
--- a/tests/suites/test_suite_asn1parse.data
+++ b/tests/suites/test_suite_asn1parse.data
@@ -172,27 +172,15 @@
 INTEGER 0, extra leading 0
 get_integer:"02020000":"0":0
 
-INTEGER -0
-depends_on:SUPPORT_NEGATIVE_INTEGERS
-get_integer:"020180":"0":0
-
 INTEGER 1
 get_integer:"020101":"1":0:
 
 INTEGER 1, extra leading 0
 get_integer:"02020001":"1":0:
 
-INTEGER -1
-depends_on:SUPPORT_NEGATIVE_INTEGERS
-get_integer:"020181":"-1":0
-
 INTEGER 0x7f
 get_integer:"02017f":"7f":0
 
-INTEGER -0x7f
-depends_on:SUPPORT_NEGATIVE_INTEGERS
-get_integer:"0201ff":"-7f":0
-
 INTEGER 0x80
 get_integer:"02020080":"80":0
 
@@ -226,6 +214,12 @@
 INTEGER with 128 value octets (leading 0 in length)
 get_integer:"028200800123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef":"0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef":0
 
+INTEGER -1
+get_integer:"0201ff":"-1":0
+
+INTEGER -0x7f
+get_integer:"020181":"-7f":0
+
 Not INTEGER
 get_integer:"010101":"":MBEDTLS_ERR_ASN1_UNEXPECTED_TAG
 
diff --git a/tests/suites/test_suite_asn1parse.function b/tests/suites/test_suite_asn1parse.function
index f794db7..defbd01 100644
--- a/tests/suites/test_suite_asn1parse.function
+++ b/tests/suites/test_suite_asn1parse.function
@@ -293,6 +293,7 @@
 #if defined(MBEDTLS_BIGNUM_C)
     mbedtls_mpi expected_mpi;
     mbedtls_mpi actual_mpi;
+    mbedtls_mpi complement;
     int expected_result_for_mpi = expected_result;
 #endif
     long expected_value;
@@ -303,6 +304,7 @@
 #if defined(MBEDTLS_BIGNUM_C)
     mbedtls_mpi_init( &expected_mpi );
     mbedtls_mpi_init( &actual_mpi );
+    mbedtls_mpi_init( &complement );
 #endif
 
     errno = 0;
@@ -314,6 +316,16 @@
 #endif
             ) )
     {
+        /* The library returns the dubious error code INVALID_LENGTH
+         * for integers that are out of range. */
+        expected_result_for_int = MBEDTLS_ERR_ASN1_INVALID_LENGTH;
+    }
+    if( expected_result == 0 && expected_value < 0 )
+    {
+        /* The library does not support negative INTEGERs and
+         * returns the dubious error code INVALID_LENGTH.
+         * Test that we preserve the historical behavior. If we
+         * decide to change the behavior, we'll also change this test. */
         expected_result_for_int = MBEDTLS_ERR_ASN1_INVALID_LENGTH;
     }
 
@@ -339,7 +351,34 @@
     TEST_EQUAL( ret, expected_result_for_mpi );
     if( ret == 0 )
     {
-        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &actual_mpi , &expected_mpi ) == 0 );
+        if( expected_value >= 0 )
+        {
+            TEST_ASSERT( mbedtls_mpi_cmp_mpi( &actual_mpi,
+                                              &expected_mpi ) == 0 );
+        }
+        else
+        {
+            /* The library ignores the sign bit in ASN.1 INTEGERs
+             * (which makes sense insofar as INTEGERs are sometimes
+             * abused as bit strings), so the result of parsing them
+             * is a positive integer such that expected_mpi +
+             * actual_mpi = 2^n where n is the length of the content
+             * of the INTEGER. (Leading ff octets don't matter for the
+             * expected value, but they matter for the actual value.)
+             * Test that we don't change from this behavior. If we
+             * decide to fix the library to change the behavior on
+             * negative INTEGERs, we'll fix this test code. */
+            unsigned char *q = input->x + 1;
+            size_t len;
+            TEST_ASSERT( mbedtls_asn1_get_len( &q, input->x + input->len,
+                                               &len ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_lset( &complement, 1 ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_shift_l( &complement, len * 8 ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_add_mpi( &complement, &complement,
+                                              &expected_mpi ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_cmp_mpi( &complement,
+                                              &actual_mpi ) == 0 );
+        }
         TEST_ASSERT( p == input->x + input->len );
     }
 #endif
@@ -348,6 +387,7 @@
 #if defined(MBEDTLS_BIGNUM_C)
     mbedtls_mpi_free( &expected_mpi );
     mbedtls_mpi_free( &actual_mpi );
+    mbedtls_mpi_free( &complement );
 #endif
     /*empty cleanup in some configurations*/ ;
 }