diff --git a/src/math/polysat/fixed_bits.cpp b/src/math/polysat/fixed_bits.cpp
new file mode 100644
index 000000000..d49916c10
--- /dev/null
+++ b/src/math/polysat/fixed_bits.cpp
@@ -0,0 +1,144 @@
+/*++
+Copyright (c) 2022 Microsoft Corporation
+
+Module Name:
+
+    Extract fixed bits from constraints
+
+Author:
+
+    Jakob Rath, Nikolaj Bjorner (nbjorner), Clemens Eisenhofer 2022-08-22
+
+--*/
+
+#include "math/polysat/fixed_bits.h"
+#include "math/polysat/ule_constraint.h"
+#include "math/polysat/clause.h"
+
+namespace polysat {
+
+    /**
+     * Constraint lhs <= rhs.
+     *
+     * 2^(k - d) * x = 2^(k - d) * c
+     * ==> x[|d|:0] = c[|d|:0]
+     *
+     * -2^(k - 2) * x > 2^(k - 1)
+     * <=> 2 + x[1:0] > 2  (mod 4)
+     * ==> x[1:0] = 1
+     *    -- TODO: Generalize [the obvious solution does not work]
+     */
+
+    /**
+     * 2^(k - d) * x = 2^(k - d) * c
+     * ==> x[|d|:0] = c[|d|:0]
+     */
+    bool get_eq_fixed_lsb(pdd const& p, fixed_bits& out) {
+        if (!p.hi().is_val())
+            return false;
+        // TODO:
+        return false;
+    }
+
+    bool get_eq_fixed_bits(pdd const& p, fixed_bits& out) {
+        return get_eq_fixed_lsb(p, out);
+    }
+
+    /**
+     * Constraint lhs <= rhs.
+     *
+     * -2^(k - 2) * x > 2^(k - 1)
+     * <=> 2 + x[1:0] > 2  (mod 4)
+     * ==> x[1:0] = 1
+     *    -- TODO: Generalize [the obvious solution does not work]
+     */
+    bool get_ule_fixed_lsb(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_bits& out) {
+        return false;
+    }
+
+    bool get_ule_fixed_bits(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_bits& out) {
+        return false;
+    }
+
+    bool get_fixed_bits(signed_constraint c, fixed_bits& out) {
+        SASSERT_EQ(c->vars().size(), 1);  // this only makes sense for univariate constraints
+        if (c->is_ule())
+            return get_ule_fixed_bits(c->to_ule().lhs(), c->to_ule().rhs(), c.is_positive(), out);
+        // if (c->is_op())
+        //     ;  // TODO:  x & constant = constant   ==> bitmask ... but we have trouble recognizing that because we introduce a new variable for '&' before we see the equality.
+        return false;
+    }
+
+
+
+
+/*
+    // 2^(k - d) * x = m * 2^(k - d)
+    // Special case [still seems to occur frequently]: -2^(k - 2) * x > 2^(k - 1) - TODO: Generalize [the obvious solution does not work] => lsb(x, 2) = 1
+    bool get_lsb(pdd lhs, pdd rhs, pdd& p, trailing_bits& info, bool pos) {
+        SASSERT(lhs.is_univariate() && lhs.degree() <= 1);
+        SASSERT(rhs.is_univariate() && rhs.degree() <= 1);
+
+        if (rhs.is_zero()) { // equality
+            auto lhs_decomp = decouple_constant(lhs);
+
+            lhs = lhs_decomp.first;
+            rhs = -lhs_decomp.second;
+
+            SASSERT(rhs.is_val());
+
+            unsigned k = lhs.manager().power_of_2();
+            unsigned d = lhs.max_pow2_divisor();
+            unsigned span = k - d;
+            if (span == 0 || lhs.is_val())
+                return false;
+
+            p = lhs.div(rational::power_of_two(d));
+            rational rhs_val = rhs.val();
+            info.bits = rhs_val / rational::power_of_two(d);
+            if (!info.bits.is_int())
+                return false;
+
+            SASSERT(lhs.is_univariate() && lhs.degree() <= 1);
+
+            auto it = p.begin();
+            auto first = *it;
+            it++;
+            if (it == p.end()) {
+                // if the lhs contains only one monomial it is of the form: odd * x = mask. We can multiply by the inverse to get the mask for x
+                SASSERT(first.coeff.is_odd());
+                rational inv;
+                VERIFY(first.coeff.mult_inverse(lhs.power_of_2(), inv));
+                p *= inv;
+                info.bits = mod2k(info.bits * inv, span);
+            }
+
+            info.length = span;
+            info.positive = pos;
+            return true;
+        }
+        else { // inequality - check for special case
+            if (pos || lhs.power_of_2() < 3)
+                return false;
+            auto it = lhs.begin();
+            if (it == lhs.end())
+                return false;
+            if (it->vars.size() != 1)
+                return false;
+            rational coeff = it->coeff;
+            it++;
+            if (it != lhs.end())
+                return false;
+            if ((mod2k(-coeff, lhs.power_of_2())) != rational::power_of_two(lhs.power_of_2() - 2))
+                return false;
+            p = lhs.div(coeff);
+            SASSERT(p.is_var());
+            info.bits = 1;
+            info.length = 2;
+            info.positive = true; // this is a conjunction
+            return true;
+        }
+    }
+*/
+
+}  // namespace polysat
diff --git a/src/math/polysat/fixed_bits.h b/src/math/polysat/fixed_bits.h
new file mode 100644
index 000000000..895ac8763
--- /dev/null
+++ b/src/math/polysat/fixed_bits.h
@@ -0,0 +1,41 @@
+/*++
+Copyright (c) 2022 Microsoft Corporation
+
+Module Name:
+
+    Extract fixed bits from (univariate) constraints
+
+Author:
+
+    Jakob Rath, Nikolaj Bjorner (nbjorner), Clemens Eisenhofer 2022-08-22
+
+--*/
+#pragma once
+#include "math/polysat/types.h"
+#include "math/polysat/constraint.h"
+#include "util/vector.h"
+
+namespace polysat {
+
+    struct fixed_bits {
+        unsigned hi = 0;
+        unsigned lo = 0;
+        rational value;
+
+        /// The constraint is equivalent to setting fixed bits on a variable.
+        // bool is_equivalent;
+
+        fixed_bits() = default;
+        fixed_bits(unsigned hi, unsigned lo, rational value): hi(hi), lo(lo), value(value) {}
+    };
+
+    using fixed_bits_vector = vector<fixed_bits>;
+
+    bool get_eq_fixed_lsb(pdd const& p, fixed_bits& out);
+    bool get_eq_fixed_bits(pdd const& p, fixed_bits& out);
+
+    bool get_ule_fixed_lsb(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_bits& out);
+    bool get_ule_fixed_bits(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_bits& out);
+    bool get_fixed_bits(signed_constraint c, fixed_bits& out);
+
+}
diff --git a/src/math/polysat/slicing.cpp b/src/math/polysat/slicing.cpp
index bf53a1bf6..25463d71f 100644
--- a/src/math/polysat/slicing.cpp
+++ b/src/math/polysat/slicing.cpp
@@ -506,7 +506,9 @@ namespace polysat {
     }
 
     bool slicing::try_get_value(enode* s, rational& val) const {
-        return m_bv->is_numeral(s->get_expr(), val);
+        bool const ok = m_bv->is_numeral(s->get_expr(), val);
+        SASSERT_EQ(ok, is_value(s));
+        return ok;
     }
 
     void slicing::explain_class(enode* x, enode* y, ptr_vector<void>& out_deps) {
@@ -1115,23 +1117,55 @@ namespace polysat {
     void slicing::add_constraint(signed_constraint c) {
         LOG(c);
         SASSERT(!is_conflict());
-        if (!c->is_eq())
+#if 0
+        if (!add_fixed_bits(c))
             return;
-        pdd const& p = c->to_eq();
+#endif
+        if (c->is_eq())
+            add_constraint_eq(c->to_eq(), c.blit());
+    }
+
+    bool slicing::add_fixed_bits(signed_constraint c) {
+        // TODO: what is missing here:
+        // - we don't prioritize constraints that set larger bit ranges
+        //   e.g., c1 sets 3 lower bits, and c2 sets 5 lower bits.
+        //   slicing may have both {c1,c2} in justifications while previously we always prefer c2.
+        // - (we could wait until propagate() to add fixed bits to the egraph. but that would only work on a single decision level.)
+        if (c->vars().size() != 1)
+            return true;
+        fixed_bits fb;
+        if (!get_fixed_bits(c, fb))
+            return true;
+        pvar const x = c->vars()[0];
+        return add_fixed_bits(x, fb.hi, fb.lo, fb.value, c.blit());
+    }
+
+    bool slicing::add_fixed_bits(pvar x, unsigned hi, unsigned lo, rational const& value, sat::literal lit) {
+        enode_vector& xs = m_tmp3;
+        SASSERT(xs.empty());
+        mk_slice(var2slice(x), hi, lo, xs, false, false);
+        enode* const sval = mk_value_slice(value, hi - lo + 1);
+        // 'xs' will be cleared by 'merge'.
+        // NOTE: the 'nullptr' argument will be fixed by 'egraph_merge'
+        return merge(xs, sval, mk_var_dep(x, nullptr, lit));
+    }
+
+    bool slicing::add_constraint_eq(pdd const& p, sat::literal lit) {
         auto& m = p.manager();
         for (auto& [a, x] : p.linear_monomials()) {
             if (a != 1 && a != m.max_value())
                 continue;
             pdd const body = a.is_one() ? (m.mk_var(x) - p) : (m.mk_var(x) + p);
             // c is either x = body or x != body, depending on polarity
-            if (!add_equation(x, body, c.blit())) {
+            if (!add_equation(x, body, lit)) {
                 SASSERT(is_conflict());
-                return;
+                return false;
             }
             // without this check, when p = x - y we would handle both x = y and y = x separately
             if (body.is_unary())
                 break;
         }
+        return true;
     }
 
     bool slicing::add_equation(pvar x, pdd const& body, sat::literal lit) {
@@ -1288,28 +1322,29 @@ namespace polysat {
         SASSERT(all_of(m_egraph.nodes(), [](enode* n) { return !n->is_marked1(); }));
     }
 
-    void slicing::collect_fixed(pvar v, rational& mask, rational& value) {
+    void slicing::collect_fixed(pvar v, fixed_bits_vector& out, euf::enode_pair_vector& out_just) {
         enode_vector& base = m_tmp2;
         SASSERT(base.empty());
         get_base(var2slice(v), base);
-        mask = 0;
-        value = 0;
         rational a;
         unsigned lo = 0;
-        for (auto it = base.rbegin(); it != base.rend(); ++it) {
-            enode* n = *it;
+        for (enode* n : base) {
             enode* r = n->get_root();
             unsigned const w = width(n);
+            unsigned const hi = lo + w - 1;
             if (try_get_value(r, a)) {
-                rational const factor = rational::power_of_two(lo);
-                // TODO: probably better to return vector of {w, lo, a} instead
-                mask += (rational::power_of_two(w) - 1) * factor;
-                value += a * factor;
+                out.push_back({hi, lo, a});
+                out_just.push_back({n, r});
             }
             lo += w;
         }
     }
 
+    void slicing::explain_fixed(euf::enode_pair const& just, std::function<void(sat::literal)> const& on_lit, std::function<void(pvar)> const& on_var) {
+        auto [n, r] = just;
+        NOT_IMPLEMENTED_YET(); // TODO: like explain_value
+    }
+
     std::ostream& slicing::display(std::ostream& out) const {
         enode_vector base;
         for (pvar v = 0; v < m_var2slice.size(); ++v) {
diff --git a/src/math/polysat/slicing.h b/src/math/polysat/slicing.h
index 15a4aacc1..97162a153 100644
--- a/src/math/polysat/slicing.h
+++ b/src/math/polysat/slicing.h
@@ -28,6 +28,7 @@ Notation:
 #include "ast/bv_decl_plugin.h"
 #include "math/polysat/types.h"
 #include "math/polysat/constraint.h"
+#include "math/polysat/fixed_bits.h"
 #include <variant>
 
 namespace polysat {
@@ -269,8 +270,11 @@ namespace polysat {
         pvar mk_concat(unsigned num_args, pvar const* args, pvar replay_var);
         void replay_concat(unsigned num_args, pvar const* args, pvar r);
 
+        bool add_constraint_eq(pdd const& p, sat::literal lit);
         bool add_equation(pvar x, pdd const& body, sat::literal lit);
         bool add_value(pvar v, rational const& value, sat::literal lit);
+        bool add_fixed_bits(signed_constraint c);
+        bool add_fixed_bits(pvar x, unsigned hi, unsigned lo, rational const& value, sat::literal lit);
 
         bool invariant() const;
         bool invariant_needs_congruence() const;
@@ -335,7 +339,8 @@ namespace polysat {
         void collect_simple_overlaps(pvar v, pvar_vector& out);
 
         /** Collect fixed portions of the variable v */
-        void collect_fixed(pvar v, rational& mask, rational& value);
+        void collect_fixed(pvar v, fixed_bits_vector& out, euf::enode_pair_vector& out_just);
+        void explain_fixed(euf::enode_pair const& just, std::function<void(sat::literal)> const& on_lit, std::function<void(pvar)> const& on_var);
 
         std::ostream& display(std::ostream& out) const;
         std::ostream& display_tree(std::ostream& out) const;
diff --git a/src/math/polysat/viable.cpp b/src/math/polysat/viable.cpp
index 2bf1697e5..0d8145e37 100644
--- a/src/math/polysat/viable.cpp
+++ b/src/math/polysat/viable.cpp
@@ -976,14 +976,17 @@ namespace {
 #if 0
         // TODO: wip
         fixed_bits_vector fbs;
-        s.m_slicing.collect_fixed(v, fbs);
+        euf::enode_pair_vector fbs_just;
+        s.m_slicing.collect_fixed(v, fbs, fbs_just);
 
-        for (fixed_bits const& fb : fbs) {
+        for (unsigned idx = fbs.size(); idx-- > 0; ) {
+            fixed_bits const& fb = fbs[idx];
+            euf::enode_pair const& just = fbs_just[idx];
             for (unsigned i = fb.lo; i <= fb.hi; ++i) {
                 SASSERT(out_fbi.just_src[i].empty());  // since we don't get overlapping ranges from collect_fixed.
                 SASSERT(out_fbi.just_side_cond[i].empty());
                 out_fbi.fixed[i] = to_lbool(fb.value.get_bit(i - fb.lo));
-                // TODO: out_fbi.just_src[i].push_back(
+                // TODO: s.m_slicing.explain_fixed( ... );  with  out_fbi.just_src[i].push_back(...)
             }
         }
 #endif