diff --git a/src/Functions/FunctionHashID.h b/src/Functions/FunctionHashID.h
index 30f08c96eca..e469381a784 100644
--- a/src/Functions/FunctionHashID.h
+++ b/src/Functions/FunctionHashID.h
@@ -52,6 +52,7 @@ public:
     bool isSuitableForShortCircuitArgumentsExecution(const DataTypesWithConstInfo & /*arguments*/) const override { return false; }
 
     bool useDefaultImplementationForConstants() const override { return true; }
+    ColumnNumbers getArgumentsThatAreAlwaysConstant() const override { return {1, 2, 3}; }
 
     DataTypePtr getReturnTypeImpl(const ColumnsWithTypeAndName & arguments) const override
     {
@@ -69,7 +70,7 @@ public:
         if (arguments.size() > 1)
         {
             const auto & hash_col = arguments[1];
-            if (!isString(hash_col.type) || !isColumnConst(*hash_col.column.get()))
+            if (!isString(hash_col.type))
                 throw Exception(
                     ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                     "Second argument of function {} must be String, got {}",
@@ -80,7 +81,7 @@ public:
         if (arguments.size() > 2)
         {
             const auto & min_length_col = arguments[2];
-            if (!isUInt8(min_length_col.type) || !isColumnConst(*min_length_col.column.get()))
+            if (!isUInt8(min_length_col.type))
                 throw Exception(
                     ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                     "Third argument of function {} must be UInt8, got {}",
@@ -91,7 +92,7 @@ public:
         if (arguments.size() > 3)
         {
             const auto & alphabet_col = arguments[3];
-            if (!isString(alphabet_col.type) || !isColumnConst(*alphabet_col.column.get()))
+            if (!isString(alphabet_col.type))
                 throw Exception(
                     ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                     "Fourth argument of function {} must be String, got {}",
diff --git a/tests/queries/0_stateless/02293_hashid.reference b/tests/queries/0_stateless/02293_hashid.reference
index f36b1500288..dfc78349c05 100644
--- a/tests/queries/0_stateless/02293_hashid.reference
+++ b/tests/queries/0_stateless/02293_hashid.reference
@@ -8,5 +8,8 @@
 2	obmgndljgajpkeao
 3	dldokmpjpgjgeanb
 4	nkdlpgajngjnobme
-xkOpDGxQpVB
-jR
+YQrvD5XGvbx
+Bm3zaOq7zbp
+oV
+oV
+6b
diff --git a/tests/queries/0_stateless/02293_hashid.sql b/tests/queries/0_stateless/02293_hashid.sql
index 45aaefe7356..9938154f169 100644
--- a/tests/queries/0_stateless/02293_hashid.sql
+++ b/tests/queries/0_stateless/02293_hashid.sql
@@ -1,7 +1,16 @@
+-- Tags: no-backward-compatibility-check
 SET allow_experimental_hash_functions = 1;
 
 select number, hashid(number) from system.numbers limit 5;
 select number, hashid(number, 's3cr3t', 16, 'abcdefghijklmnop') from system.numbers limit 5;
 select hashid(1234567890123456, 's3cr3t');
+select hashid(1234567890123456, 's3cr3t2');
 
 SELECT  hashid(1, hashid(2));
+SELECT  hashid(1, 'k5');
+SELECT  hashid(1, 'k5_othersalt');
+
+-- https://github.com/ClickHouse/ClickHouse/issues/39672
+SELECT
+    JSONExtractRaw(257, NULL),
+    hashid(1024, if(rand() % 10, 'truetruetruetrue', NULL), 's3\0r3t'); -- {serverError 43}