diff --git a/pygmt/tests/test_datasets_earth_relief.py b/pygmt/tests/test_datasets_earth_relief.py
index 6e65bde902d..c8c63050a63 100644
--- a/pygmt/tests/test_datasets_earth_relief.py
+++ b/pygmt/tests/test_datasets_earth_relief.py
@@ -4,6 +4,8 @@
 import numpy as np
 import numpy.testing as npt
 import pytest
+from packaging.version import Version
+from pygmt.clib import __gmt_version__
 from pygmt.datasets import load_earth_relief
 from pygmt.exceptions import GMTInvalidInput
 
@@ -186,6 +188,10 @@ def test_earth_relief_15s_default_registration():
     npt.assert_allclose(data.max(), -71, atol=0.5)
 
 
+@pytest.mark.xfail(
+    condition=Version(__gmt_version__) >= Version("6.5.0"),
+    reason="Upstream bug tracked in https://github.com/GenericMappingTools/pygmt/issues/2511",
+)
 def test_earth_relief_03s_default_registration():
     """
     Test that the grid returned by default for the 3 arc-second resolution has a
@@ -198,5 +204,5 @@ def test_earth_relief_03s_default_registration():
     npt.assert_allclose(data.coords["lat"].data.max(), 5)
     npt.assert_allclose(data.coords["lon"].data.min(), -10)
     npt.assert_allclose(data.coords["lon"].data.max(), -9.8)
-    npt.assert_allclose(data.min(), -2131.9, atol=0.5)
+    npt.assert_allclose(data.min(), -2069.85, atol=0.5)
     npt.assert_allclose(data.max(), -924.5, atol=0.5)
diff --git a/pygmt/tests/test_datasets_load_remote_datasets.py b/pygmt/tests/test_datasets_load_remote_datasets.py
index ee5e126a0de..3d68518f18d 100644
--- a/pygmt/tests/test_datasets_load_remote_datasets.py
+++ b/pygmt/tests/test_datasets_load_remote_datasets.py
@@ -2,6 +2,8 @@
 Test the _load_remote_dataset function.
 """
 import pytest
+from packaging.version import Version
+from pygmt.clib import __gmt_version__
 from pygmt.datasets.load_remote_dataset import _load_remote_dataset
 from pygmt.exceptions import GMTInvalidInput
 
@@ -27,11 +29,13 @@ def test_load_remote_dataset_benchmark_with_region():
     data = load_remote_dataset_wrapper(resolution="01d", region=[-10, 10, -5, 5])
     assert data.name == "seafloor_age"
     assert data.attrs["long_name"] == "age of seafloor crust"
-    assert data.attrs["cpt"] == "@earth_age.cpt"
     assert data.attrs["units"] == "Myr"
     assert data.attrs["horizontal_datum"] == "WGS84"
     assert data.gmt.registration == 0
     assert data.shape == (11, 21)
+    # The cpt attribute was added since GMT 6.4.0
+    if Version(__gmt_version__) >= Version("6.4.0"):
+        assert data.attrs["cpt"] == "@earth_age.cpt"
 
 
 def test_load_remote_dataset_invalid_resolutions():
diff --git a/pygmt/tests/test_x2sys_cross.py b/pygmt/tests/test_x2sys_cross.py
index 7aa2e4653c0..af9c7ac8dcd 100644
--- a/pygmt/tests/test_x2sys_cross.py
+++ b/pygmt/tests/test_x2sys_cross.py
@@ -10,7 +10,9 @@
 import numpy.testing as npt
 import pandas as pd
 import pytest
+from packaging.version import Version
 from pygmt import x2sys_cross, x2sys_init
+from pygmt.clib import __gmt_version__
 from pygmt.datasets import load_sample_data
 from pygmt.exceptions import GMTInvalidInput
 from pygmt.helpers import data_kind
@@ -55,6 +57,10 @@ def test_x2sys_cross_input_file_output_file():
 
 
 @pytest.mark.usefixtures("mock_x2sys_home")
+@pytest.mark.xfail(
+    condition=Version(__gmt_version__) < Version("6.5.0"),
+    reason="Upstream bug fixed in https://github.com/GenericMappingTools/gmt/pull/8188",
+)
 def test_x2sys_cross_input_file_output_dataframe():
     """
     Run x2sys_cross by passing in a filename, and output internal crossovers to a
@@ -196,6 +202,10 @@ def test_x2sys_cross_invalid_tracks_input_type(tracks):
 
 
 @pytest.mark.usefixtures("mock_x2sys_home")
+@pytest.mark.xfail(
+    condition=Version(__gmt_version__) < Version("6.5.0"),
+    reason="Upstream bug fixed in https://github.com/GenericMappingTools/gmt/pull/8188",
+)
 def test_x2sys_cross_region_interpolation_numpoints():
     """
     Test that x2sys_cross's region (R), interpolation (l) and numpoints (W) arguments
@@ -221,6 +231,10 @@ def test_x2sys_cross_region_interpolation_numpoints():
 
 
 @pytest.mark.usefixtures("mock_x2sys_home")
+@pytest.mark.xfail(
+    condition=Version(__gmt_version__) < Version("6.5.0"),
+    reason="Upstream bug fixed in https://github.com/GenericMappingTools/gmt/pull/8188",
+)
 def test_x2sys_cross_trackvalues():
     """
     Test that x2sys_cross's trackvalues (Z) argument work.