diff --git a/src/smt/seq/nseq_parikh.cpp b/src/smt/seq/nseq_parikh.cpp
index 9ee4690b8..13efbd94a 100644
--- a/src/smt/seq/nseq_parikh.cpp
+++ b/src/smt/seq/nseq_parikh.cpp
@@ -241,6 +241,18 @@ namespace seq {
         expr_ref zero(arith.mk_int(0), m);
         out.push_back(int_constraint(k_var, zero,
                                      int_constraint_kind::ge, mem.m_dep, m));
+
+        // Constraint 3 (optional): k ≤ max_k when max_len is bounded.
+        // max_k = floor((max_len - min_len) / stride)
+        // This gives the solver an explicit upper bound on k, which tightens
+        // the search space when combined with other constraints on len(str).
+        if (max_len != UINT_MAX) {
+            unsigned range = max_len - min_len;  // max_len >= min_len here
+            unsigned max_k = range / stride;
+            expr_ref max_k_expr(arith.mk_int(max_k), m);
+            out.push_back(int_constraint(k_var, max_k_expr,
+                                         int_constraint_kind::le, mem.m_dep, m));
+        }
     }
 
     void nseq_parith::apply_to_node(nielsen_node& node) {
@@ -251,4 +263,63 @@ namespace seq {
             node.add_int_constraint(ic);
     }
 
+    // -----------------------------------------------------------------------
+    // Quick Parikh feasibility check (no solver call)
+    // -----------------------------------------------------------------------
+
+    // Returns true if a Parikh conflict is detected: there exists a membership
+    // str ∈ re for a single-variable str where the modular length constraint
+    //   len(str) = min_len + stride * k  (k ≥ 0)
+    // is inconsistent with the variable's current integer bounds [lb, ub].
+    //
+    // This check is lightweight — it uses only modular arithmetic on the already-
+    // known regex min/max lengths and the per-variable bounds stored in the node.
+    bool nseq_parith::check_parikh_conflict(nielsen_node& node) {
+        seq_util& seq = m_sg.get_seq_util();
+
+        for (str_mem const& mem : node.str_mems()) {
+            if (!mem.m_str || !mem.m_regex || !mem.m_str->is_var())
+                continue;
+
+            expr* re_expr = mem.m_regex->get_expr();
+            if (!re_expr || !seq.is_re(re_expr))
+                continue;
+
+            unsigned min_len = seq.re.min_length(re_expr);
+            unsigned max_len = seq.re.max_length(re_expr);
+            if (min_len >= max_len) continue; // fixed or empty — no stride constraint
+
+            unsigned stride = compute_length_stride(re_expr);
+            if (stride <= 1) continue; // no useful modular constraint
+
+            unsigned lb = node.var_lb(mem.m_str);
+            unsigned ub = node.var_ub(mem.m_str);
+
+            // Check: ∃k ≥ 0 such that lb ≤ min_len + stride * k ≤ ub ?
+            //
+            // First find the smallest k satisfying the lower bound:
+            //   k_min = 0                          if min_len ≥ lb
+            //   k_min = ⌈(lb - min_len) / stride⌉  otherwise
+            //
+            // Then verify min_len + stride * k_min ≤ ub.
+            unsigned k_min = 0;
+            if (lb > min_len) {
+                unsigned gap = lb - min_len;
+                k_min = (gap + stride - 1) / stride;  // ceiling division
+            }
+
+            // Overflow guard: stride * k_min may overflow unsigned.
+            unsigned len_at_k_min;
+            if (k_min > (UINT_MAX - min_len) / stride) {
+                // Overflow: min_len + stride * k_min > UINT_MAX ≥ ub → conflict.
+                return true;
+            }
+            len_at_k_min = min_len + stride * k_min;
+
+            if (ub != UINT_MAX && len_at_k_min > ub)
+                return true; // no valid k exists → Parikh conflict
+        }
+        return false;
+    }
+
 } // namespace seq
diff --git a/src/smt/seq/nseq_parith.h b/src/smt/seq/nseq_parith.h
index 6f8fc7ae3..e10e5b6eb 100644
--- a/src/smt/seq/nseq_parith.h
+++ b/src/smt/seq/nseq_parith.h
@@ -91,6 +91,7 @@ namespace seq {
         // When stride > 1 and min_len < max_len (bounds don't pin length):
         //   adds: len(str) = min_len + stride · k   (equality)
         //         k ≥ 0                              (non-negativity)
+        //         k ≤ (max_len - min_len) / stride   (upper bound, when max_len bounded)
         // These tighten the integer constraint set for the subsolver.
         // Dependencies are copied from mem.m_dep.
         void generate_parikh_constraints(str_mem const& mem,
@@ -101,6 +102,22 @@ namespace seq {
         // and appends the resulting int_constraints to node.int_constraints().
         void apply_to_node(nielsen_node& node);
 
+        // Quick Parikh feasibility check (no solver call).
+        //
+        // For each single-variable membership str ∈ re, checks whether the
+        // modular constraint  len(str) = min_len + stride · k  (k ≥ 0)
+        // has any solution given the current per-variable bounds stored in
+        // node.var_lb(str) and node.var_ub(str).
+        //
+        // Returns true when a conflict is detected (no valid k exists for
+        // some membership).  The caller should then mark the node with
+        // backtrack_reason::parikh_image.
+        //
+        // This is a lightweight pre-check that avoids calling the integer
+        // subsolver.  It is sound (never returns true for a satisfiable node)
+        // but incomplete (may miss conflicts that require the full solver).
+        bool check_parikh_conflict(nielsen_node& node);
+
         // Compute the length stride of a regex expression.
         // Exposed for testing and external callers.
         unsigned get_length_stride(expr* re) { return compute_length_stride(re); }
diff --git a/src/smt/seq/seq_nielsen.cpp b/src/smt/seq/seq_nielsen.cpp
index 6a2c730ca..98f114fa6 100644
--- a/src/smt/seq/seq_nielsen.cpp
+++ b/src/smt/seq/seq_nielsen.cpp
@@ -20,6 +20,7 @@ Author:
 --*/
 
 #include "smt/seq/seq_nielsen.h"
+#include "smt/seq/nseq_parith.h"
 #include "ast/arith_decl_plugin.h"
 #include "ast/ast_pp.h"
 #include "util/hashtable.h"
@@ -431,10 +432,12 @@ namespace seq {
 
     nielsen_graph::nielsen_graph(euf::sgraph& sg, simple_solver& solver):
         m_sg(sg),
-        m_solver(solver) {
+        m_solver(solver),
+        m_parith(alloc(nseq_parith, sg)) {
     }
 
     nielsen_graph::~nielsen_graph() {
+        dealloc(m_parith);
         reset();
     }
 
@@ -1032,6 +1035,23 @@ namespace seq {
     // nielsen_graph: search
     // -----------------------------------------------------------------------
 
+    void nielsen_graph::apply_parikh_to_node(nielsen_node& node) {
+        if (node.m_parikh_applied) return;
+        node.m_parikh_applied = true;
+
+        // Generate modular length constraints (len(str) = min_len + stride·k, etc.)
+        // and append them to the node's integer constraint list.
+        m_parith->apply_to_node(node);
+
+        // Lightweight feasibility pre-check: does the Parikh modular constraint
+        // contradict the variable's current integer bounds?  If so, mark this
+        // node as a Parikh-image conflict immediately (avoids a solver call).
+        if (!node.is_currently_conflict() && m_parith->check_parikh_conflict(node)) {
+            node.m_is_general_conflict = true;
+            node.m_reason = backtrack_reason::parikh_image;
+        }
+    }
+
     void nielsen_graph::assert_root_constraints_to_solver() {
         if (m_root_constraints_asserted) return;
         m_root_constraints_asserted = true;
@@ -1129,6 +1149,15 @@ namespace seq {
             return search_result::sat;
         }
 
+        // Apply Parikh image filter: generate modular length constraints and
+        // perform a lightweight feasibility pre-check.  The filter is guarded
+        // internally (m_parikh_applied) so it only runs once per node.
+        apply_parikh_to_node(*node);
+        if (node->is_currently_conflict()) {
+            ++m_stats.m_num_simplify_conflict;
+            return search_result::unsat;
+        }
+
         // integer feasibility check: collect side constraints along the path
         // and verify they are jointly satisfiable using the LP solver
         if (!cur_path.empty() && !check_int_feasibility(node, cur_path)) {
diff --git a/src/smt/seq/seq_nielsen.h b/src/smt/seq/seq_nielsen.h
index 1660be312..70ab76edc 100644
--- a/src/smt/seq/seq_nielsen.h
+++ b/src/smt/seq/seq_nielsen.h
@@ -248,6 +248,7 @@ namespace seq {
     class nielsen_node;
     class nielsen_edge;
     class nielsen_graph;
+    class nseq_parith;  // Parikh image filter (defined in nseq_parith.h)
 
     /**
      * Abstract interface for an incremental solver used by nielsen_graph
@@ -519,6 +520,10 @@ namespace seq {
         // evaluation index for run tracking
         unsigned                m_eval_idx = 0;
 
+        // Parikh filter: set to true once apply_parikh_to_node has been applied
+        // to this node. Prevents duplicate constraint generation across DFS runs.
+        bool                    m_parikh_applied = false;
+
     public:
         nielsen_node(nielsen_graph* graph, unsigned id);
 
@@ -711,6 +716,10 @@ namespace seq {
         // Set to true after assert_root_constraints_to_solver() is first called.
         bool                          m_root_constraints_asserted = false;
 
+        // Parikh image filter: generates modular length constraints from regex
+        // memberships.  Allocated in the constructor; owned by this graph.
+        nseq_parith*                  m_parith = nullptr;
+
     public:
         // Construct with a caller-supplied solver.  Ownership is NOT transferred;
         // the caller is responsible for keeping the solver alive.
@@ -816,6 +825,16 @@ namespace seq {
     private:
         search_result search_dfs(nielsen_node* node, unsigned depth, svector<nielsen_edge*>& cur_path);
 
+        // Apply the Parikh image filter to a node: generate modular length
+        // constraints from regex memberships and append them to the node's
+        // int_constraints.  Also performs a lightweight feasibility pre-check;
+        // if a Parikh conflict is detected the node's conflict flag is set with
+        // backtrack_reason::parikh_image.
+        //
+        // Guarded by node.m_parikh_applied so that constraints are generated
+        // only once per node across DFS iterations.
+        void apply_parikh_to_node(nielsen_node& node);
+
         // create a fresh variable with a unique name
         euf::snode* mk_fresh_var();