diff --git a/lib/checknullpointer.cpp b/lib/checknullpointer.cpp
index acf2f642e..f3cf18706 100644
--- a/lib/checknullpointer.cpp
+++ b/lib/checknullpointer.cpp
@@ -367,6 +367,15 @@ void CheckNullPointer::nullPointerStructByDeRefAndChec()
             skipvar.insert(tok1->varId());
             continue;
         }
+        else if (Token::Match(tok1, "( ! %var% ||") ||
+                 Token::Match(tok1, "( %var% &&"))
+        {
+            tok1 = tok1->next();
+            if (tok1->str() == "!")
+                tok1 = tok1->next();
+            skipvar.insert(tok1->varId());
+            continue;
+        }
 
         /**
          * @todo There are lots of false negatives here. A dereference
@@ -564,6 +573,10 @@ void CheckNullPointer::nullPointerByDeRefAndChec()
                     if (Token::Match(tok1->link()->previous(), "while ( %varid%", varid))
                         break;
 
+                    if (Token::Match(tok1->link(), "( ! %varid% ||", varid) ||
+                        Token::Match(tok1->link(), "( %varid% &&", varid))
+                        break;
+
                     if (Token::simpleMatch(tok1->link()->previous(), "sizeof ("))
                     {
                         tok1 = tok1->link()->previous();
diff --git a/test/testnullpointer.cpp b/test/testnullpointer.cpp
index 9a01034ab..0a5f7ebda 100644
--- a/test/testnullpointer.cpp
+++ b/test/testnullpointer.cpp
@@ -385,6 +385,13 @@ private:
               "    }\n"
               "}");
         ASSERT_EQUALS("", errout.str());
+
+        // #3128
+        check("void f(ABC *abc) {\n"
+              "    x(!abc || y(abc->a));\n"
+              "    if (abc) {}\n"
+              "}");
+        ASSERT_EQUALS("", errout.str());
     }
 
     // Dereferencing a pointer and then checking if it is null
@@ -524,6 +531,19 @@ private:
               "}");
         ASSERT_EQUALS("", errout.str());
 
+        // #3128 - false positive
+        check("void f(int *p) {\n"
+              "    assert(!p || (*p<=6));\n"
+              "    if (p) { *p = 0; }\n"
+              "}");
+        ASSERT_EQUALS("", errout.str());
+
+        check("void f(int *p) {\n"
+              "    assert(p && (*p<=6));\n"
+              "    if (p) { *p = 0; }\n"
+              "}");
+        ASSERT_EQUALS("", errout.str());
+
         check("void foo(x *p)\n"
               "{\n"
               "    p = p->next;\n"