diff --git a/src/solvers/smt2_incremental/convert_expr_to_smt.cpp b/src/solvers/smt2_incremental/convert_expr_to_smt.cpp
index 18ddc576f12..6d5fb84fd93 100644
--- a/src/solvers/smt2_incremental/convert_expr_to_smt.cpp
+++ b/src/solvers/smt2_incremental/convert_expr_to_smt.cpp
@@ -121,6 +121,16 @@ static smt_termt convert_c_bool_cast(
     smt_bit_vector_constant_termt{0, c_bool_width});
 }
 
+static std::function<std::function<smt_termt(smt_termt)>(std::size_t)>
+extension_for_type(const typet &type)
+{
+  if(can_cast_type<signedbv_typet>(type))
+    return smt_bit_vector_theoryt::sign_extend;
+  if(can_cast_type<unsignedbv_typet>(type))
+    return smt_bit_vector_theoryt::zero_extend;
+  UNREACHABLE;
+}
+
 static smt_termt make_bitvector_resize_cast(
   const smt_termt &from_term,
   const bitvector_typet &from_type,
@@ -147,10 +157,7 @@ static smt_termt make_bitvector_resize_cast(
   if(to_width < from_width)
     return smt_bit_vector_theoryt::extract(to_width - 1, 0)(from_term);
   const std::size_t extension_size = to_width - from_width;
-  if(can_cast_type<signedbv_typet>(from_type))
-    return smt_bit_vector_theoryt::sign_extend(extension_size)(from_term);
-  else
-    return smt_bit_vector_theoryt::zero_extend(extension_size)(from_term);
+  return extension_for_type(from_type)(extension_size)(from_term);
 }
 
 struct sort_based_cast_to_bit_vector_convertert final
@@ -652,34 +659,61 @@ static smt_termt convert_expr_to_smt(const index_exprt &index)
     "Generation of SMT formula for index expression: " + index.pretty());
 }
 
+template <typename factoryt, typename shiftt>
+static smt_termt
+convert_to_smt_shift(const factoryt &factory, const shiftt &shift)
+{
+  const smt_termt first_operand = convert_expr_to_smt(shift.op0());
+  const smt_termt second_operand = convert_expr_to_smt(shift.op1());
+  const auto first_bit_vector_sort =
+    first_operand.get_sort().cast<smt_bit_vector_sortt>();
+  const auto second_bit_vector_sort =
+    second_operand.get_sort().cast<smt_bit_vector_sortt>();
+  INVARIANT(
+    first_bit_vector_sort && second_bit_vector_sort,
+    "Shift expressions are expected to have bit vector operands.");
+  const std::size_t first_width = first_bit_vector_sort->bit_width();
+  const std::size_t second_width = second_bit_vector_sort->bit_width();
+  if(first_width > second_width)
+  {
+    return factory(
+      first_operand,
+      extension_for_type(shift.op1().type())(first_width - second_width)(
+        second_operand));
+  }
+  else if(first_width < second_width)
+  {
+    return factory(
+      extension_for_type(shift.op0().type())(second_width - first_width)(
+        first_operand),
+      second_operand);
+  }
+  else
+  {
+    return factory(first_operand, second_operand);
+  }
+}
+
 static smt_termt convert_expr_to_smt(const shift_exprt &shift)
 {
-  // TODO: Dispatch into different types of shifting
-  const auto &first_operand = shift.op0();
-  const auto &second_operand = shift.op1();
-
+  // TODO: Dispatch for rotation expressions. A `shift_exprt` can be a rotation.
   if(const auto left_shift = expr_try_dynamic_cast<shl_exprt>(shift))
   {
-    return smt_bit_vector_theoryt::shift_left(
-      convert_expr_to_smt(first_operand), convert_expr_to_smt(second_operand));
+    return convert_to_smt_shift(
+      smt_bit_vector_theoryt::shift_left, *left_shift);
   }
-  else if(
-    const auto right_logical_shift = expr_try_dynamic_cast<lshr_exprt>(shift))
+  if(const auto right_logical_shift = expr_try_dynamic_cast<lshr_exprt>(shift))
   {
-    return smt_bit_vector_theoryt::logical_shift_right(
-      convert_expr_to_smt(first_operand), convert_expr_to_smt(second_operand));
+    return convert_to_smt_shift(
+      smt_bit_vector_theoryt::logical_shift_right, *right_logical_shift);
   }
-  else if(
-    const auto right_arith_shift = expr_try_dynamic_cast<ashr_exprt>(shift))
+  if(const auto right_arith_shift = expr_try_dynamic_cast<ashr_exprt>(shift))
   {
-    return smt_bit_vector_theoryt::arithmetic_shift_right(
-      convert_expr_to_smt(first_operand), convert_expr_to_smt(second_operand));
-  }
-  else
-  {
-    UNIMPLEMENTED_FEATURE(
-      "Generation of SMT formula for shift expression: " + shift.pretty());
+    return convert_to_smt_shift(
+      smt_bit_vector_theoryt::arithmetic_shift_right, *right_arith_shift);
   }
+  UNIMPLEMENTED_FEATURE(
+    "Generation of SMT formula for shift expression: " + shift.pretty());
 }
 
 static smt_termt convert_expr_to_smt(const with_exprt &with)
@@ -733,6 +767,11 @@ static smt_termt convert_expr_to_smt(const extractbit_exprt &extract_bit)
 
 static smt_termt convert_expr_to_smt(const extractbits_exprt &extract_bits)
 {
+  const smt_termt from = convert_expr_to_smt(extract_bits.src());
+  const auto upper_value = numeric_cast<std::size_t>(extract_bits.upper());
+  const auto lower_value = numeric_cast<std::size_t>(extract_bits.lower());
+  if(upper_value && lower_value)
+    return smt_bit_vector_theoryt::extract(*upper_value, *lower_value)(from);
   UNIMPLEMENTED_FEATURE(
     "Generation of SMT formula for extract bits expression: " +
     extract_bits.pretty());
diff --git a/unit/solvers/smt2_incremental/convert_expr_to_smt.cpp b/unit/solvers/smt2_incremental/convert_expr_to_smt.cpp
index 3aec501617d..3b7393f5ce5 100644
--- a/unit/solvers/smt2_incremental/convert_expr_to_smt.cpp
+++ b/unit/solvers/smt2_incremental/convert_expr_to_smt.cpp
@@ -819,6 +819,105 @@ SCENARIO(
   }
 }
 
+TEST_CASE(
+  "expr to smt conversion for shifts of mismatched operands.",
+  "[core][smt2_incremental]")
+{
+  using make_typet = std::function<typet(std::size_t)>;
+  const make_typet make_unsigned = constructor_oft<unsignedbv_typet>{};
+  const make_typet make_signed = constructor_oft<signedbv_typet>{};
+  using make_extensiont =
+    std::function<std::function<smt_termt(smt_termt)>(std::size_t)>;
+  const make_extensiont zero_extend = smt_bit_vector_theoryt::zero_extend;
+  const make_extensiont sign_extend = smt_bit_vector_theoryt::sign_extend;
+  std::string type_description;
+  make_typet make_type;
+  make_extensiont make_extension;
+  using type_rowt = std::tuple<std::string, make_typet, make_extensiont>;
+  std::tie(type_description, make_type, make_extension) = GENERATE_REF(
+    type_rowt{"Unsigned operands.", make_unsigned, zero_extend},
+    type_rowt{"Signed operands.", make_signed, sign_extend});
+  SECTION(type_description)
+  {
+    using make_shift_exprt = std::function<exprt(exprt, exprt)>;
+    const make_shift_exprt left_shift_expr = constructor_of<shl_exprt>();
+    const make_shift_exprt arithmetic_right_shift_expr =
+      constructor_of<ashr_exprt>();
+    const make_shift_exprt logical_right_shift_expr =
+      constructor_of<lshr_exprt>();
+    using make_shift_termt = std::function<smt_termt(smt_termt, smt_termt)>;
+    const make_shift_termt left_shift_term = smt_bit_vector_theoryt::shift_left;
+    const make_shift_termt arithmetic_right_shift_term =
+      smt_bit_vector_theoryt::arithmetic_shift_right;
+    const make_shift_termt logical_right_shift_term =
+      smt_bit_vector_theoryt::logical_shift_right;
+    std::string shift_description;
+    make_shift_exprt make_shift_expr;
+    make_shift_termt make_shift_term;
+    using shift_rowt =
+      std::tuple<std::string, make_shift_exprt, make_shift_termt>;
+    std::tie(shift_description, make_shift_expr, make_shift_term) =
+      GENERATE_REF(
+        shift_rowt{"Left shift.", left_shift_expr, left_shift_term},
+        shift_rowt{
+          "Arithmetic right shift.",
+          arithmetic_right_shift_expr,
+          arithmetic_right_shift_term},
+        shift_rowt{
+          "Logical right shift.",
+          logical_right_shift_expr,
+          logical_right_shift_term});
+    SECTION(shift_description)
+    {
+      SECTION("Wider left hand side")
+      {
+        const exprt input = make_shift_expr(
+          symbol_exprt{"foo", make_type(32)},
+          symbol_exprt{"bar", make_type(8)});
+        INFO("Input expr: " + input.pretty(2, 0));
+        const smt_termt expected_result = make_shift_term(
+          smt_identifier_termt{"foo", smt_bit_vector_sortt{32}},
+          make_extension(24)(
+            smt_identifier_termt{"bar", smt_bit_vector_sortt{8}}));
+        CHECK(convert_expr_to_smt(input) == expected_result);
+      }
+      SECTION("Wider right hand side")
+      {
+        const exprt input = make_shift_expr(
+          symbol_exprt{"foo", make_type(8)},
+          symbol_exprt{"bar", make_type(32)});
+        INFO("Input expr: " + input.pretty(2, 0));
+        const smt_termt expected_result = make_shift_term(
+          make_extension(24)(
+            smt_identifier_termt{"foo", smt_bit_vector_sortt{8}}),
+          smt_identifier_termt{"bar", smt_bit_vector_sortt{32}});
+        CHECK(convert_expr_to_smt(input) == expected_result);
+      }
+    }
+  }
+}
+
+TEST_CASE(
+  "expr to smt conversion for extract bits expressions",
+  "[core][smt2_incremental]")
+{
+  const typet operand_type = unsignedbv_typet{8};
+  const exprt input = extractbits_exprt{
+    symbol_exprt{"foo", operand_type},
+    from_integer(4, operand_type),
+    from_integer(2, operand_type),
+    unsignedbv_typet{3}};
+  const smt_termt expected_result = smt_bit_vector_theoryt::extract(4, 2)(
+    smt_identifier_termt{"foo", smt_bit_vector_sortt{8}});
+  CHECK(convert_expr_to_smt(input) == expected_result);
+  const cbmc_invariants_should_throwt invariants_throw;
+  CHECK_THROWS(convert_expr_to_smt(extractbits_exprt{
+    symbol_exprt{"foo", operand_type},
+    symbol_exprt{"bar", operand_type},
+    symbol_exprt{"bar", operand_type},
+    unsignedbv_typet{3}}));
+}
+
 TEST_CASE("expr to smt conversion for type casts", "[core][smt2_incremental]")
 {
   const symbol_exprt bool_expr{"foo", bool_typet{}};