diff --git a/backends/rtlil/rtlil_backend.cc b/backends/rtlil/rtlil_backend.cc
index 057edc584..d47bebf82 100644
--- a/backends/rtlil/rtlil_backend.cc
+++ b/backends/rtlil/rtlil_backend.cc
@@ -61,7 +61,9 @@ void RTLIL_BACKEND::dump_const(std::ostream &f, const RTLIL::Const &data, int wi
 				return;
 			}
 		}
-		f << stringf("%d'", width);
+		if ((data.flags & RTLIL::CONST_FLAG_UNSIZED) == 0) {
+			f << stringf("%d'", width);
+		}
 		if (data.flags & RTLIL::CONST_FLAG_SIGNED) {
 			f << stringf("s");
 		}
@@ -173,9 +175,10 @@ void RTLIL_BACKEND::dump_cell(std::ostream &f, std::string indent, const RTLIL::
 	dump_attributes(f, indent, cell);
 	f << stringf("%s" "cell %s %s\n", indent, cell->type, cell->name);
 	for (const auto& [name, param] : reversed(cell->parameters)) {
-		f << stringf("%s  parameter%s%s %s ", indent,
+		f << stringf("%s  parameter%s%s%s %s ", indent,
 				(param.flags & RTLIL::CONST_FLAG_SIGNED) != 0 ? " signed" : "",
 				(param.flags & RTLIL::CONST_FLAG_REAL) != 0 ? " real" : "",
+				(param.flags & RTLIL::CONST_FLAG_UNSIZED) != 0 ? " unsized" : "",
 				name);
 		dump_const(f, param);
 		f << stringf("\n");
diff --git a/frontends/ast/ast.cc b/frontends/ast/ast.cc
index 4a16abee9..984c4294c 100644
--- a/frontends/ast/ast.cc
+++ b/frontends/ast/ast.cc
@@ -993,6 +993,8 @@ RTLIL::Const AstNode::asParaConst() const
 	RTLIL::Const val = asAttrConst();
 	if (is_signed)
 		val.flags |= RTLIL::CONST_FLAG_SIGNED;
+	if (is_unsized)
+		val.flags |= RTLIL::CONST_FLAG_UNSIZED;
 	return val;
 }
 
@@ -1766,7 +1768,10 @@ static std::string serialize_param_value(const RTLIL::Const &val) {
 		res.push_back('s');
 	if (val.flags & RTLIL::ConstFlags::CONST_FLAG_REAL)
 		res.push_back('r');
-	res += stringf("%d", GetSize(val));
+	if (val.flags & RTLIL::ConstFlags::CONST_FLAG_UNSIZED)
+		res.push_back('u');
+	else
+		res += stringf("%d", GetSize(val));
 	res.push_back('\'');
 	res.append(val.as_string("?"));
 	return res;
@@ -1860,7 +1865,7 @@ std::string AstModule::derive_common(RTLIL::Design *design, const dict<RTLIL::Id
 		} else if ((it->second.flags & RTLIL::CONST_FLAG_STRING) != 0)
 			child->children[0] = AstNode::mkconst_str(loc, it->second.decode_string());
 		else
-			child->children[0] = AstNode::mkconst_bits(loc, it->second.to_bits(), (it->second.flags & RTLIL::CONST_FLAG_SIGNED) != 0);
+			child->children[0] = AstNode::mkconst_bits(loc, it->second.to_bits(), (it->second.flags & RTLIL::CONST_FLAG_SIGNED) != 0, (it->second.flags & RTLIL::CONST_FLAG_UNSIZED) != 0);
 		rewritten.insert(it->first);
 	}
 
diff --git a/frontends/ast/simplify.cc b/frontends/ast/simplify.cc
index 308406591..83174e963 100644
--- a/frontends/ast/simplify.cc
+++ b/frontends/ast/simplify.cc
@@ -2265,9 +2265,13 @@ bool AstNode::simplify(bool const_fold, int stage, int width_hint, bool sign_hin
 			}
 			if (children[0]->type == AST_CONSTANT) {
 				if (width != int(children[0]->bits.size())) {
-					RTLIL::SigSpec sig(children[0]->bits);
-					sig.extend_u0(width, children[0]->is_signed);
-					children[0] = mkconst_bits(location, sig.as_const().to_bits(), is_signed);
+					RTLIL::Const val;
+					if (children[0]->is_unsized) {
+						val = children[0]->bitsAsUnsizedConst(width);
+					} else {
+						val = children[0]->bitsAsConst(width);
+					}
+					children[0] = mkconst_bits(location, val.to_bits(), is_signed);
 					fixup_hierarchy_flags();
 				}
 				children[0]->is_signed = is_signed;
diff --git a/frontends/rtlil/rtlil_frontend.cc b/frontends/rtlil/rtlil_frontend.cc
index 04d01fc93..271962725 100644
--- a/frontends/rtlil/rtlil_frontend.cc
+++ b/frontends/rtlil/rtlil_frontend.cc
@@ -567,10 +567,13 @@ struct RTLILFrontendWorker {
 			if (try_parse_keyword("parameter")) {
 				bool is_signed = false;
 				bool is_real = false;
+				bool is_unsized = false;
 				if (try_parse_keyword("signed")) {
 					is_signed = true;
 				} else if (try_parse_keyword("real")) {
 					is_real = true;
+				} else if (try_parse_keyword("unsized")) {
+					is_unsized = true;
 				}
 				RTLIL::IdString param_name = parse_id();
 				RTLIL::Const val = parse_const();
@@ -578,6 +581,8 @@ struct RTLILFrontendWorker {
 					val.flags |= RTLIL::CONST_FLAG_SIGNED;
 				if (is_real)
 					val.flags |= RTLIL::CONST_FLAG_REAL;
+				if (is_unsized)
+					val.flags |= RTLIL::CONST_FLAG_UNSIZED;
 				cell->parameters.insert({std::move(param_name), std::move(val)});
 				expect_eol();
 			} else if (try_parse_keyword("connect")) {
diff --git a/kernel/rtlil.h b/kernel/rtlil.h
index 79cc73e45..27f610f85 100644
--- a/kernel/rtlil.h
+++ b/kernel/rtlil.h
@@ -53,10 +53,11 @@ namespace RTLIL
 	// Semantic metadata - how can this constant be interpreted?
 	// Values may be generally non-exclusive
 	enum ConstFlags : unsigned char {
-		CONST_FLAG_NONE   = 0,
-		CONST_FLAG_STRING = 1,
-		CONST_FLAG_SIGNED = 2,  // only used for parameters
-		CONST_FLAG_REAL   = 4   // only used for parameters
+		CONST_FLAG_NONE    = 0,
+		CONST_FLAG_STRING  = 1,
+		CONST_FLAG_SIGNED  = 2,  // only used for parameters
+		CONST_FLAG_REAL    = 4,  // only used for parameters
+		CONST_FLAG_UNSIZED = 8,  // only used for parameters
 	};
 
 	enum SelectPartials : unsigned char {
diff --git a/tests/rtlil/everything.v b/tests/rtlil/everything.v
index 666d630c2..c4f8c348a 100644
--- a/tests/rtlil/everything.v
+++ b/tests/rtlil/everything.v
@@ -38,3 +38,20 @@ module foo(
     assign b = bb;
     assign y = a + bb;
 endmodule
+
+module set_param #(
+    parameter [3:0] VALUE = 1'bx
+) (
+    output logic [3:0] out
+);
+    assign out = VALUE;
+endmodule
+
+module use_param (
+    output logic [3:0] a, b, c, d
+);
+    set_param #($signed(1)) spa (a);
+    set_param #('1) spb (b);
+    set_param #(1.1) spc (c);
+    set_param #(1'b1) spd (d);
+endmodule
diff --git a/tests/verilog/unbased_unsized.sv b/tests/verilog/unbased_unsized.sv
index 1d0c5a72c..62f7d41ff 100644
--- a/tests/verilog/unbased_unsized.sv
+++ b/tests/verilog/unbased_unsized.sv
@@ -5,7 +5,20 @@ module pass_through(
     assign out = inp;
 endmodule
 
+module set_param #(
+    parameter logic [63:0] VALUE
+) (
+    output logic [63:0] out
+);
+    assign out = VALUE;
+endmodule
+
 module top;
+    localparam logic [63:0]
+        l01 = '0,
+        l02 = '1,
+        l03 = 'x,
+        l04 = 'z;
     logic [63:0]
         o01, o02, o03, o04,
         o05, o06, o07, o08,
@@ -23,6 +36,10 @@ module top;
     pass_through pt10('1, o10);
     pass_through pt11('x, o11);
     pass_through pt12('z, o12);
+    set_param #('0) sp13(o13);
+    set_param #('1) sp14(o14);
+    set_param #('x) sp15(o15);
+    set_param #('z) sp16(o16);
     always @* begin
         assert (o01 === {64 {1'b0}});
         assert (o02 === {64 {1'b1}});
@@ -36,5 +53,13 @@ module top;
         assert (o10 === {64 {1'b1}});
         assert (o11 === {64 {1'bx}});
         assert (o12 === {64 {1'bz}});
+        assert (l01 === {64 {1'b0}});
+        assert (l02 === {64 {1'b1}});
+        assert (l03 === {64 {1'bx}});
+        assert (l04 === {64 {1'bz}});
+        assert (o13 === {64 {1'b0}});
+        assert (o14 === {64 {1'b1}});
+        assert (o15 === {64 {1'bx}});
+        assert (o16 === {64 {1'bz}});
     end
 endmodule
diff --git a/tests/verilog/unbased_unsized.ys b/tests/verilog/unbased_unsized.ys
index 3290650d5..851866140 100644
--- a/tests/verilog/unbased_unsized.ys
+++ b/tests/verilog/unbased_unsized.ys
@@ -1,5 +1,5 @@
 read_verilog -sv unbased_unsized.sv
-hierarchy
+hierarchy -top top
 proc
 flatten
 opt -full