diff --git a/src/Standards/Squiz/Sniffs/Objects/ObjectInstantiationSniff.php b/src/Standards/Squiz/Sniffs/Objects/ObjectInstantiationSniff.php
index ea4970dbf8..84facf0540 100644
--- a/src/Standards/Squiz/Sniffs/Objects/ObjectInstantiationSniff.php
+++ b/src/Standards/Squiz/Sniffs/Objects/ObjectInstantiationSniff.php
@@ -48,21 +48,37 @@ public function process(File $phpcsFile, $stackPtr)
         $prev = $phpcsFile->findPrevious($allowedTokens, ($stackPtr - 1), null, true);
 
         $allowedTokens = [
-            T_EQUAL        => true,
-            T_DOUBLE_ARROW => true,
-            T_FN_ARROW     => true,
-            T_MATCH_ARROW  => true,
-            T_THROW        => true,
-            T_RETURN       => true,
-            T_INLINE_THEN  => true,
-            T_INLINE_ELSE  => true,
+            T_EQUAL          => T_EQUAL,
+            T_COALESCE_EQUAL => T_COALESCE_EQUAL,
+            T_DOUBLE_ARROW   => T_DOUBLE_ARROW,
+            T_FN_ARROW       => T_FN_ARROW,
+            T_MATCH_ARROW    => T_MATCH_ARROW,
+            T_THROW          => T_THROW,
+            T_RETURN         => T_RETURN,
         ];
 
-        if (isset($allowedTokens[$tokens[$prev]['code']]) === false) {
-            $error = 'New objects must be assigned to a variable';
-            $phpcsFile->addError($error, $stackPtr, 'NotAssigned');
+        if (isset($allowedTokens[$tokens[$prev]['code']]) === true) {
+            return;
         }
 
+        $ternaryLikeTokens = [
+            T_COALESCE    => true,
+            T_INLINE_THEN => true,
+            T_INLINE_ELSE => true,
+        ];
+
+        // For ternary like tokens, walk a little further back to see if it is preceded by
+        // one of the allowed tokens (within the same statement).
+        if (isset($ternaryLikeTokens[$tokens[$prev]['code']]) === true) {
+            $hasAllowedBefore = $phpcsFile->findPrevious($allowedTokens, ($prev - 1), null, false, null, true);
+            if ($hasAllowedBefore !== false) {
+                return;
+            }
+        }
+
+        $error = 'New objects must be assigned to a variable';
+        $phpcsFile->addError($error, $stackPtr, 'NotAssigned');
+
     }//end process()
 
 
diff --git a/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.inc b/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.inc
index f58af275cd..41c881289d 100644
--- a/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.inc
+++ b/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.inc
@@ -23,6 +23,24 @@ function returnMatch() {
     }
 }
 
+// Issue 3333.
+$time2 ??= new \DateTime();
+$time3 = $time1 ?? new \DateTime();
+$time3 = $time1 ?? $time2 ?? new \DateTime();
+
+function_call($time1 ?? new \DateTime());
+$return = function_call($time1 ?? new \DateTime()); // False negative depending on interpretation of the sniff.
+
+function returnViaTernary() {
+    return ($y == false ) ? ($x === true ? new Foo : new Bar) : new FooBar;
+}
+
+function nonAssignmentTernary() {
+    if (($x ? new Foo() : new Bar) instanceof FooBar) {
+        // Do something.
+    }
+}
+
 // Intentional parse error. This must be the last test in the file.
 function new
 ?>
diff --git a/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.php b/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.php
index fa32521c85..f9979fa29f 100644
--- a/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.php
+++ b/src/Standards/Squiz/Tests/Objects/ObjectInstantiationUnitTest.php
@@ -26,8 +26,10 @@ class ObjectInstantiationUnitTest extends AbstractSniffUnitTest
     public function getErrorList()
     {
         return [
-            5 => 1,
-            8 => 1,
+            5  => 1,
+            8  => 1,
+            31 => 1,
+            39 => 2,
         ];
 
     }//end getErrorList()