diff --git a/src/solvers/Makefile b/src/solvers/Makefile
index ccf66d4cfa6..6c46d6e048f 100644
--- a/src/solvers/Makefile
+++ b/src/solvers/Makefile
@@ -128,6 +128,7 @@ SRC = $(BOOLEFORCE_SRC) \
       flattening/boolbv_unary_minus.cpp \
       flattening/boolbv_union.cpp \
       flattening/boolbv_update.cpp \
+      flattening/boolbv_update_bit.cpp \
       flattening/boolbv_update_bits.cpp \
       flattening/boolbv_width.cpp \
       flattening/boolbv_with.cpp \
diff --git a/src/solvers/flattening/boolbv.cpp b/src/solvers/flattening/boolbv.cpp
index 3f026d4b3b7..64a9816c9ba 100644
--- a/src/solvers/flattening/boolbv.cpp
+++ b/src/solvers/flattening/boolbv.cpp
@@ -109,6 +109,8 @@ bvt boolbvt::convert_bitvector(const exprt &expr)
     return convert_with(to_with_expr(expr));
   else if(expr.id()==ID_update)
     return convert_update(to_update_expr(expr));
+  else if(expr.id() == ID_update_bit)
+    return convert_update_bit(to_update_bit_expr(expr));
   else if(expr.id()==ID_case)
     return convert_case(expr);
   else if(expr.id()==ID_cond)
diff --git a/src/solvers/flattening/boolbv.h b/src/solvers/flattening/boolbv.h
index 5992bdc4b0d..48d32ece23b 100644
--- a/src/solvers/flattening/boolbv.h
+++ b/src/solvers/flattening/boolbv.h
@@ -39,6 +39,7 @@ class overflow_result_exprt;
 class replication_exprt;
 class unary_overflow_exprt;
 class union_typet;
+class update_bit_exprt;
 class update_bits_exprt;
 
 class boolbvt:public arrayst
@@ -177,6 +178,7 @@ class boolbvt:public arrayst
   virtual bvt convert_member(const member_exprt &expr);
   virtual bvt convert_with(const with_exprt &expr);
   virtual bvt convert_update(const update_exprt &);
+  virtual bvt convert_update_bit(const update_bit_exprt &);
   virtual bvt convert_update_bits(const update_bits_exprt &);
   virtual bvt convert_case(const exprt &expr);
   virtual bvt convert_cond(const cond_exprt &);
diff --git a/src/solvers/flattening/boolbv_update_bit.cpp b/src/solvers/flattening/boolbv_update_bit.cpp
new file mode 100644
index 00000000000..2fd6feee706
--- /dev/null
+++ b/src/solvers/flattening/boolbv_update_bit.cpp
@@ -0,0 +1,16 @@
+/*******************************************************************\
+
+Module:
+
+Author: Daniel Kroening, dkr@amazon.com
+
+\*******************************************************************/
+
+#include <util/bitvector_expr.h>
+
+#include "boolbv.h"
+
+bvt boolbvt::convert_update_bit(const update_bit_exprt &expr)
+{
+  return convert_bv(expr.lower());
+}
diff --git a/src/solvers/flattening/boolbv_with.cpp b/src/solvers/flattening/boolbv_with.cpp
index f04bf78575a..5eb83b0b3c0 100644
--- a/src/solvers/flattening/boolbv_with.cpp
+++ b/src/solvers/flattening/boolbv_with.cpp
@@ -22,9 +22,32 @@ bvt boolbvt::convert_with(const with_exprt &expr)
     type.id() == ID_bv || type.id() == ID_unsignedbv ||
     type.id() == ID_signedbv)
   {
+    if(expr.operands().size() > 3)
+    {
+      std::size_t s = expr.operands().size();
+
+      // strip off the trailing two operands
+      with_exprt tmp = expr;
+      tmp.operands().resize(s - 2);
+
+      with_exprt new_with_expr(
+        tmp, expr.operands()[s - 2], expr.operands().back());
+
+      // recursive call
+      return convert_with(new_with_expr);
+    }
+
     PRECONDITION(expr.operands().size() == 3);
-    return convert_bv(
-      update_bits_exprt(expr.old(), expr.where(), expr.new_value()));
+    if(expr.new_value().type().id() == ID_bool)
+    {
+      return convert_bv(
+        update_bit_exprt(expr.old(), expr.where(), expr.new_value()));
+    }
+    else
+    {
+      return convert_bv(
+        update_bits_exprt(expr.old(), expr.where(), expr.new_value()));
+    }
   }
 
   bvt bv = convert_bv(expr.old());
diff --git a/src/solvers/smt2/smt2_conv.cpp b/src/solvers/smt2/smt2_conv.cpp
index 5ddc20ce70f..16967c683cc 100644
--- a/src/solvers/smt2/smt2_conv.cpp
+++ b/src/solvers/smt2/smt2_conv.cpp
@@ -1685,6 +1685,10 @@ void smt2_convt::convert_expr(const exprt &expr)
   {
     convert_update(to_update_expr(expr));
   }
+  else if(expr.id() == ID_update_bit)
+  {
+    convert_update_bit(to_update_bit_expr(expr));
+  }
   else if(expr.id() == ID_update_bits)
   {
     convert_update_bits(to_update_bits_expr(expr));
@@ -4290,8 +4294,16 @@ void smt2_convt::convert_with(const with_exprt &expr)
           expr_type.id()==ID_unsignedbv ||
           expr_type.id()==ID_signedbv)
   {
-    convert_update_bits(
-      update_bits_exprt(expr.old(), expr.where(), expr.new_value()));
+    if(expr.new_value().type().id() == ID_bool)
+    {
+      convert_update_bit(
+        update_bit_exprt(expr.old(), expr.where(), expr.new_value()));
+    }
+    else
+    {
+      convert_update_bits(
+        update_bits_exprt(expr.old(), expr.where(), expr.new_value()));
+    }
   }
   else
     UNEXPECTEDCASE(
@@ -4306,6 +4318,11 @@ void smt2_convt::convert_update(const update_exprt &expr)
   SMT2_TODO("smt2_convt::convert_update to be implemented");
 }
 
+void smt2_convt::convert_update_bit(const update_bit_exprt &expr)
+{
+  return convert_expr(expr.lower());
+}
+
 void smt2_convt::convert_update_bits(const update_bits_exprt &expr)
 {
   return convert_expr(expr.lower());
diff --git a/src/solvers/smt2/smt2_conv.h b/src/solvers/smt2/smt2_conv.h
index 406b18cf8d1..4a043824831 100644
--- a/src/solvers/smt2/smt2_conv.h
+++ b/src/solvers/smt2/smt2_conv.h
@@ -32,6 +32,7 @@ Author: Daniel Kroening, kroening@kroening.com
 class floatbv_typecast_exprt;
 class ieee_float_op_exprt;
 class union_typet;
+class update_bit_exprt;
 class update_bits_exprt;
 
 class smt2_convt : public stack_decision_proceduret
@@ -150,6 +151,7 @@ class smt2_convt : public stack_decision_proceduret
 
   void convert_with(const with_exprt &expr);
   void convert_update(const update_exprt &);
+  void convert_update_bit(const update_bit_exprt &);
   void convert_update_bits(const update_bits_exprt &);
 
   void convert_expr(const exprt &);
diff --git a/src/util/bitvector_expr.cpp b/src/util/bitvector_expr.cpp
index eb8fa4807a5..c62a50e594c 100644
--- a/src/util/bitvector_expr.cpp
+++ b/src/util/bitvector_expr.cpp
@@ -42,6 +42,34 @@ extractbits_exprt::extractbits_exprt(
     from_integer(_lower, integer_typet()));
 }
 
+exprt update_bit_exprt::lower() const
+{
+  const auto width = to_bitvector_type(type()).get_width();
+  auto src_bv_type = bv_typet(width);
+
+  // build a mask 0...0 1
+  auto mask_bv =
+    make_bvrep(width, [](std::size_t index) { return index == 0; });
+  auto mask_expr = constant_exprt(mask_bv, src_bv_type);
+
+  // shift the mask by the index
+  auto mask_shifted = shl_exprt(mask_expr, index());
+
+  auto src_masked = bitand_exprt(
+    typecast_exprt(src(), src_bv_type), bitnot_exprt(mask_shifted));
+
+  // zero-extend the replacement bit to match src
+  auto new_value_casted = typecast_exprt(
+    typecast_exprt(new_value(), unsignedbv_typet(width)), src_bv_type);
+
+  // shift the replacement bits
+  auto new_value_shifted = shl_exprt(new_value_casted, index());
+
+  // or the masked src and the shifted replacement bits
+  return typecast_exprt(
+    bitor_exprt(src_masked, new_value_shifted), src().type());
+}
+
 exprt update_bits_exprt::lower() const
 {
   const auto width = to_bitvector_type(type()).get_width();
diff --git a/src/util/bitvector_expr.h b/src/util/bitvector_expr.h
index 3d40b356798..1276bf287ff 100644
--- a/src/util/bitvector_expr.h
+++ b/src/util/bitvector_expr.h
@@ -531,6 +531,93 @@ inline extractbits_exprt &to_extractbits_expr(exprt &expr)
   return ret;
 }
 
+/// \brief Replaces a sub-range of a bit-vector operand
+class update_bit_exprt : public expr_protectedt
+{
+public:
+  /// Replaces the bit [\p _index] from \p _src to produce a result of
+  /// the same type as \p _src. The index counts from the
+  /// least-significant bit. Updates outside of the range of \p _src
+  /// yield an expression equal to \p _src.
+  update_bit_exprt(exprt _src, exprt _index, exprt _new_value)
+    : expr_protectedt(
+        ID_update_bit,
+        _src.type(),
+        {_src, std::move(_index), std::move(_new_value)})
+  {
+    PRECONDITION(new_value().type().id() == ID_bool);
+  }
+
+  update_bit_exprt(exprt _src, const std::size_t _index, exprt _new_value);
+
+  exprt &src()
+  {
+    return op0();
+  }
+
+  exprt &index()
+  {
+    return op1();
+  }
+
+  exprt &new_value()
+  {
+    return op2();
+  }
+
+  const exprt &src() const
+  {
+    return op0();
+  }
+
+  const exprt &index() const
+  {
+    return op1();
+  }
+
+  const exprt &new_value() const
+  {
+    return op2();
+  }
+
+  static void check(
+    const exprt &expr,
+    const validation_modet vm = validation_modet::INVARIANT)
+  {
+    validate_operands(expr, 3, "update_bit must have three operands");
+  }
+
+  /// A lowering to masking, shifting, or.
+  exprt lower() const;
+};
+
+template <>
+inline bool can_cast_expr<update_bit_exprt>(const exprt &base)
+{
+  return base.id() == ID_update_bit;
+}
+
+/// \brief Cast an exprt to an \ref update_bit_exprt
+///
+/// \a expr must be known to be \ref update_bit_exprt.
+///
+/// \param expr: Source expression
+/// \return Object of type \ref update_bit_exprt
+inline const update_bit_exprt &to_update_bit_expr(const exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_update_bit);
+  update_bit_exprt::check(expr);
+  return static_cast<const update_bit_exprt &>(expr);
+}
+
+/// \copydoc to_update_bit_expr(const exprt &)
+inline update_bit_exprt &to_update_bit_expr(exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_update_bit);
+  update_bit_exprt::check(expr);
+  return static_cast<update_bit_exprt &>(expr);
+}
+
 /// \brief Replaces a sub-range of a bit-vector operand
 class update_bits_exprt : public expr_protectedt
 {
diff --git a/src/util/irep_ids.def b/src/util/irep_ids.def
index c06f6293055..eea285397a5 100644
--- a/src/util/irep_ids.def
+++ b/src/util/irep_ids.def
@@ -185,6 +185,7 @@ IREP_ID_ONE(exists)
 IREP_ID_ONE(repeat)
 IREP_ID_ONE(extractbit)
 IREP_ID_ONE(extractbits)
+IREP_ID_ONE(update_bit)
 IREP_ID_ONE(update_bits)
 IREP_ID_TWO(C_reference, #reference)
 IREP_ID_TWO(C_rvalue_reference, #rvalue_reference)