diff --git a/src/System.Net.Primitives/tests/FunctionalTests/IPAddressParsing.cs b/src/System.Net.Primitives/tests/FunctionalTests/IPAddressParsing.cs
index ede268af38ef..4baf57e0e3c6 100644
--- a/src/System.Net.Primitives/tests/FunctionalTests/IPAddressParsing.cs
+++ b/src/System.Net.Primitives/tests/FunctionalTests/IPAddressParsing.cs
@@ -346,9 +346,6 @@ public void TryParseIPv6_ValidAddress_RoundtripMatchesExpected(string address, s
 
         public static IEnumerable<object[]> InvalidIpv6Addresses()
         {
-            yield return new object[] { "" }; // malformed
-            yield return new object[] { "[" }; // malformed
-            yield return new object[] { "[]" }; // malformed
             yield return new object[] { "[:]" }; // malformed
             yield return new object[] { ":::4df" };
             yield return new object[] { "4df:::" };
@@ -442,6 +439,9 @@ public void ParseIPv6_InvalidAddress_ThrowsFormatException(string invalidAddress
             new object[] { "%12" }, // just scope
             new object[] { "[192.168.0.1]" }, // raw v4
             new object[] { "[1]" }, // incomplete
+            new object[] { "" }, // malformed
+            new object[] { "[" }, // malformed
+            new object[] { "[]" }, // malformed
         };
 
         [Theory]
diff --git a/src/System.Private.Uri/tests/FunctionalTests/IriTest.cs b/src/System.Private.Uri/tests/FunctionalTests/IriTest.cs
index 061b31bee0f1..f188ae495103 100644
--- a/src/System.Private.Uri/tests/FunctionalTests/IriTest.cs
+++ b/src/System.Private.Uri/tests/FunctionalTests/IriTest.cs
@@ -647,6 +647,7 @@ public static IEnumerable<Object[]> Iri_ExpandingContents_TooLong
 
         [Theory]
         [MemberData(nameof(Iri_ExpandingContents_TooLong))]
+        [SkipOnTargetFramework(TargetFrameworkMonikers.NetFramework, "Disable until the .NET FX CI machines get the latest patches.")]
         public static void Iri_ExpandingContents_ThrowsIfTooLong(string input)
         {
             Assert.Throws<System.UriFormatException>(() => { Uri itemUri = new Uri(input); });
diff --git a/src/System.Private.Uri/tests/FunctionalTests/UriIpHostTest.cs b/src/System.Private.Uri/tests/FunctionalTests/UriIpHostTest.cs
index 8641fed7a940..2f952f89ec52 100644
--- a/src/System.Private.Uri/tests/FunctionalTests/UriIpHostTest.cs
+++ b/src/System.Private.Uri/tests/FunctionalTests/UriIpHostTest.cs
@@ -321,7 +321,6 @@ public void UriIPv6Host_EmbeddedIPv4_Success(string address, string expected)
         [InlineData(":1:2:3:4:5")] // leading single colon
         [InlineData(":1:2:3:4:5:6")] // leading single colon
         [InlineData(":1:2:3:4:5:6:7")] // leading single colon
-        [InlineData(":1:2:3:4:5:6:7:8")] // leading single colon
         [InlineData(":1:2:3:4:5:6:7:8:9")] // leading single colon
         [InlineData("::1:2:3:4:5:6:7:8")] // compressor with too many number groups
         [InlineData("1::2:3:4:5:6:7:8")] // compressor with too many number groups
@@ -352,6 +351,14 @@ public void UriIPv6Host_BadAddress(string address)
             ParseBadIPv6Address(address);
         }
 
+        [Theory]
+        [InlineData(":1:2:3:4:5:6:7:8")] // leading single colon
+        [SkipOnTargetFramework(TargetFrameworkMonikers.NetFramework, "Full framework machines are not yet patched with the fix for this")]
+        public void UriIPv6Host_BadAddress_SkipOnFramework(string address)
+        {
+            ParseBadIPv6Address(address);
+        }
+
         #region Helpers
 
         private void ParseIPv6Address(string ipv6String)