diff --git a/lib/templatesimplifier.cpp b/lib/templatesimplifier.cpp
index db7808927..3816925ea 100644
--- a/lib/templatesimplifier.cpp
+++ b/lib/templatesimplifier.cpp
@@ -748,6 +748,26 @@ bool TemplateSimplifier::simplifyCalculations(Token *_tokens)
         }
 
         if (tok->isNumber()) {
+            // Remove redundant conditions (0&&x) (1||x)
+            if (Token::Match(tok->previous(), "[(=,] 0 &&") ||
+                Token::Match(tok->previous(), "[(=,] 1 ||")) {
+                unsigned int par = 0;
+                const Token *tok2 = tok;
+                for (tok2 = tok; tok2; tok2 = tok2->next()) {
+                    if (tok2->str() == "(")
+                        ++par;
+                    else if (tok2->str() == ")") {
+                        if (par == 0)
+                            break;
+                        --par;
+                    } else if (par == 0 && (Token::Match(tok2, "[,;]")))
+                        break;
+                }
+                if (Token::Match(tok2, "[);,]"))
+                    Token::eraseTokens(tok, tok2);
+                continue;
+            }
+
             if (tok->str() == "0") {
                 if (Token::Match(tok->previous(), "[+-|] 0")) {
                     tok = tok->previous();
@@ -766,7 +786,6 @@ bool TemplateSimplifier::simplifyCalculations(Token *_tokens)
                     tok->deleteThis();
                     ret = true;
                 } else if (Token::Match(tok->previous(), "[=[(,] 0 * %any% ,|]|)|;|=|%op%") ||
-                           Token::Match(tok->previous(), "[=[(,] 0 && %any% ,|]|)|;|=|%op%") ||
                            Token::Match(tok->previous(), "return|case 0 * %any% ,|:|;|=|%op%") ||
                            Token::Match(tok->previous(), "return|case 0 && %any% ,|:|;|=|%op%")) {
                     tok->deleteNext();
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 20318f75b..50367e51e 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -393,7 +393,7 @@ private:
 
         TEST_CASE(simplifyLogicalOperators);
 
-        TEST_CASE(simplifyCalculations); // ticket #2870
+        TEST_CASE(simplifyCalculations);
 
         // foo(p = new char[10]);  =>  p = new char[10]; foo(p);
         TEST_CASE(simplifyAssignmentInFunctionCall);
@@ -6348,7 +6348,11 @@ private:
                       tokenizeAndStringify("int foo ( ) { int i; int j; i = 1 || j; return i; }", true));
 
         ASSERT_EQUALS("int foo ( ) { return 0 ; }",
-                      tokenizeAndStringify("int foo ( ) { int i; int j; i = 0 && j; return i; }", true));
+                      tokenizeAndStringify("int foo ( ) { int i; int j; i = 0 && j; return i; }", true));        // ticket #3576 - False positives in boolean expressions
+
+        // ticket #3723 - Simplify condition (0 && a < 123)
+        ASSERT_EQUALS("( 0 )",
+                      tokenizeAndStringify("( 0 && a < 123 )", true));
     }
 
     void simplifyCompoundAssignment() {