diff --git a/qpms/bessel.c b/qpms/bessel.c
index 000ee49..2b047d4 100644
--- a/qpms/bessel.c
+++ b/qpms/bessel.c
@@ -84,7 +84,8 @@ qpms_errno_t qpms_sph_bessel_realx_fill(qpms_bessel_t typ, qpms_l_t lmax, double
 
 // TODO DOC
 qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex double x, complex double *res) {
-  if(!cimag(x))
+  if(!cimag(x) && 
+        creal(x) < 10000) // For large arguments (around 30000 or more), gsl_sf_bessel_jl_steed_array fails
     return qpms_sph_bessel_realx_fill(typ, lmax, creal(x), res);
   else if (isnan(creal(x)) || isnan(cimag(x))) 
     for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = NAN + I*NAN;
@@ -128,9 +129,17 @@ try_again: ;
       for (qpms_l_t l = 0; l <= lmax; ++l)
         res[l] = prefac * (cyr[l] + I * cyi[l]);
       if (ierr == 3) 
-        QPMS_WARN("Amos's zbes%c computation done but losses of significance "
-            "by argument reduction produce less than half of machine accuracy.", 
-            kindchar);
+        if (creal(x) >= 10000) {
+          QPMS_WARN_ONCE("Due to large argument, "
+                "Amos's zbes%c computation done but losses of significance "
+                "by argument reduction produce less than half of machine accuracy. "
+                "This warning is shown only once.", 
+                kindchar);
+        } else {
+          QPMS_WARN("Amos's zbes%c computation done but losses of significance "
+                "by argument reduction produce less than half of machine accuracy.", 
+                kindchar);
+        }
       return QPMS_SUCCESS; //TODO maybe something else if ierr == 3
     }
     else {
diff --git a/qpms/qpms_error.h b/qpms/qpms_error.h
index 0cf9f22..f554035 100644
--- a/qpms/qpms_error.h
+++ b/qpms/qpms_error.h
@@ -67,6 +67,19 @@ qpms_dbgmsg_flags qpms_dbgmsg_enable(qpms_dbgmsg_flags types);
  */
 #define QPMS_WARN(msg, ...) qpms_warn_at_flf(__FILE__,__LINE__,__func__,msg, ##__VA_ARGS__)
 
+/// Print a warning to stderr and flush the buffer – only once per run (or current thread).
+/**
+ * The arguments are the same as in standard printf().
+ */
+#define QPMS_WARN_ONCE(msg, ...) {\
+	static _Bool already_bitched = 0; \
+	if (QPMS_UNLIKELY(!already_bitched)) {\
+		qpms_warn_at_flf(__FILE__,__LINE__,__func__,msg, ##__VA_ARGS__);\
+		already_bitched = 1;\
+	}\
+}
+
+
 /// Print a debugging message to stderr and flush the buffer.
 /**
  * The arguments after \a type are the same as in standard printf().